This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 11 Conic Sections – Quiz 5 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 11 Conic Sections Quiz 5 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. A/An ..... is the set of all points in a plane that are the same distance from a fixed point called the focus and a fixed line called the directrix. A) Ellipse. B) Hyperbola. C) Parabola. D) Circle. Show Answer Correct Answer: C) Parabola. 2. Identify the conic section described by the equation 2x$^{2}$ + 8x-4y + 5 = 0. A) Ellipse. B) Parabola. C) Hyperbola. D) Circle. Show Answer Correct Answer: B) Parabola. 3. Find the vertex, focus, and directrix of the parabola:-(1/40)x$^{2}$ = y A) Vertex:(0, 0) Focus:(0, 10) Directrix:y=-10. B) Vertex:(0, 0) Focus:(-20, 0) Directrix:x = 10. C) Vertex:(0, 0) Focus:(0, 10) Directrix:y=10. D) Vertex:(0, 0) Focus:(0, -10) Directrix:y = 10. Show Answer Correct Answer: D) Vertex:(0, 0) Focus:(0, -10) Directrix:y = 10. 4. If the plane intersects the double right circular cone at its VERTEX THE ELLIPSE becomes a ..... ? A) TWO INTERSECTING LINES. B) POINT. C) CIRCLE. D) LINE. Show Answer Correct Answer: B) POINT. 5. There are only three types of conic sections. Which of the following is not a type of conic section? A) Parabola. B) Hyperbola. C) Ellipse. D) Circle. Show Answer Correct Answer: D) Circle. 6. What is the definition of a co-vertex in a hyperbola? A) A point where the hyperbola intersects its transverse axis. B) A point where the hyperbola intersects its conjugate axis. C) A point that defines the asymptotes of the hyperbola. D) A point that represents the center of the hyperbola. Show Answer Correct Answer: B) A point where the hyperbola intersects its conjugate axis. 7. Which conic section is represented by the equation2x$^{2}$ + 3y$^{2}$-6= 0? A) Hyperbola. B) Parabola. C) Ellipse. D) Circle. Show Answer Correct Answer: C) Ellipse. 8. A circle is a special type of an ellipse. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 9. What is p for this parabola? $(x-6)^2=20(y-1)$ A) P=6. B) P=5. C) P=4. D) P=20. Show Answer Correct Answer: B) P=5. 10. The length of the major axis is 6, what is the value of the first denominator in the equation? A) 12. B) 9. C) 3. D) 6. Show Answer Correct Answer: B) 9. 11. What type of conic section does the polar equation $r = \frac{5}{1 + 2\cos(\theta)}$ A) Ellipse. B) Circle. C) Parabola. D) Hyperbola. Show Answer Correct Answer: D) Hyperbola. 12. It is a set of all points in the plane that are equidistant from a fixed point. A) CIRCLE. B) PARABOLA. C) HYPERBOLA. D) ELLIPSE. Show Answer Correct Answer: A) CIRCLE. 13. Write the equation of a hyperbola with foci (-4, -5) and (8, -5) and a transverse axis length of 10. A) $\frac{\left(y+5\right)^2}{11}-\frac{\left(x-2\right)^2}{25}=1$. B) $\frac{\left(y+5\right)^2}{25}-\frac{\left(x-2\right)^2}{11}=1$. C) $\frac{\left(x-2\right)^2}{11}-\frac{\left(y+5\right)^2}{25}=1$. D) $\frac{\left(x-2\right)^2}{25}-\frac{\left(y+5\right)^2}{11}=1$. Show Answer Correct Answer: D) $\frac{\left(x-2\right)^2}{25}-\frac{\left(y+5\right)^2}{11}=1$. 14. Find the center of the circle $x^2-2x+y^2+10y+17=0$ A) (-1, 5). B) (5, -1). C) (-5, 1). D) (1, -5). Show Answer Correct Answer: D) (1, -5). 15. What is the standard form of the following equation? $4x^2+8x-9y^2+36y-176=0$ A) $\frac{\left(x-1\right)^2}{36}-\frac{\left(y-2\right)^2}{16}=1$. B) $\frac{\left(x+1\right)^2}{9}-\frac{\left(y+2\right)^2}{16}=1$. C) $\frac{\left(x+1\right)^2}{36}-\frac{\left(y-2\right)^2}{16}=1$. D) $\frac{\left(x-1\right)^2}{16}-\frac{\left(y+2\right)^2}{36}=1$. Show Answer Correct Answer: C) $\frac{\left(x+1\right)^2}{36}-\frac{\left(y-2\right)^2}{16}=1$. 16. The equation of a hyperbola with foci on the x axis is A) $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. B) $x^2+y^2=\left(a^2+b^2\right)$. C) $x^2-y^2=\left(a^2+b^2\right)$. D) $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. Show Answer Correct Answer: D) $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. 17. A/An ..... is the set of all points in a plane such that the absolute value of the difference of distances from two fixed points is constant. A) Circle. B) Hyperbola. C) Parabola. D) Ellipse. Show Answer Correct Answer: B) Hyperbola. 18. Write the equation of a circle in standard form:center:$\left(-15, 3\sqrt[]{7}\right)$ $8\pi$ A) $\left(x+15\right)^2+\left(y-3\sqrt{7}\right)^2=16$. B) (x+15)2+(y-37)2=16 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\left(x+15\right)^2+\left(y-3\sqrt{7}\right)^2=16$. 19. Identify the given conic sections that the equation represents. $9x^2+4y^2-54x-8y-59=0$ A) Ellipse. B) Circle. C) Parabola. D) Hyperbola. Show Answer Correct Answer: A) Ellipse. 20. What is the area of a sector of a circle with a radius of 8 inches and formed by a central angle that measures 60$^\circ$? A) $\frac{16\pi}{3}$. B) $\frac{64\pi}{3}$. C) $\frac{8\pi}{3}$. D) $\frac{32\pi}{3}$. Show Answer Correct Answer: D) $\frac{32\pi}{3}$. 21. Identify the conic section described by the equation $x^2-4y^2=16$ A) Circle. B) Ellipse. C) Hyperbola. D) Parabola. Show Answer Correct Answer: C) Hyperbola. 22. The parabola y = x$^{2}$-2x + 4 will A) Open up. B) Open down. C) All the above. D) None of the above. Show Answer Correct Answer: A) Open up. 23. Find the center of the circle $x^2+y^2-2x+4y+1=0$ A) (-2, 1). B) (2, -1). C) (-1, 2). D) (1, -2). Show Answer Correct Answer: D) (1, -2). 24. The equation of the hyperbola whose vertices are 2 units from the center and whose transverse axis is vertical, with asymptotes $y=\pm2x$ A) $\frac{x^2}{4}-y^2=1$. B) $\frac{y^2}{4}-x^2=1$. C) $y^2-\frac{x^2}{4}=1$. D) $x^2-\frac{y^2}{4}=1$. Show Answer Correct Answer: B) $\frac{y^2}{4}-x^2=1$. 25. Write the equation of a hyperbola with conjugate axis endpoints (-6, -1) and (0, -1) and a transverse axis length of 4. A) $\frac{\left(x+3\right)^2}{9}-\frac{\left(y+1\right)^2}{4}=1$. B) $\frac{\left(x+3\right)^2}{4}-\frac{\left(y+1\right)^2}{9}=1$. C) $\frac{\left(y+1\right)^2}{9}-\frac{\left(x+3\right)^2}{4}=1$. D) $\frac{\left(y+1\right)^2}{4}-\frac{\left(x+3\right)^2}{9}=1$. Show Answer Correct Answer: D) $\frac{\left(y+1\right)^2}{4}-\frac{\left(x+3\right)^2}{9}=1$. 26. What are the different degenerate conic sections? A) Point, line, three intersecting line. B) Point, line, five intersecting lines. C) Point, line, four intersecting lines. D) Point, line, two intersecting line. Show Answer Correct Answer: D) Point, line, two intersecting line. 27. Find the vertex, focus, and directrix of the parabola:$^{}$x$^{2}$ = 28y A) Vertex:(0, 0) Focus:(0, 7) Directrix:y=-7. B) Vertex:(0, 0) Focus:(7, 0) Directrix:x=7. C) Vertex:(0, 0) Focus:(7, 0) Directrix:y=7. D) Vertex:(0, 0) Focus:(0, -7) Directrix:x=-7. Show Answer Correct Answer: A) Vertex:(0, 0) Focus:(0, 7) Directrix:y=-7. 28. Write the equation of a circle in standard form:center:$\left(-11, -14\right)$ $16\pi$ A) $\left(x+11\right)^2+\left(y+14\right)^2=16$. B) (x+11)2+(y+14)2=16 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\left(x+11\right)^2+\left(y+14\right)^2=16$. 29. If a parabola has a focus at (-3, 0) and a vertex at the origin ..... what is the equation of the directrix? A) X=3. B) X=-3. C) Y=3. D) Y=-3. Show Answer Correct Answer: A) X=3. 30. What is the coordinate of the focus? (x+3)$^{2}$ = 4(y+5) A) (-3, -6). B) (-2, 5). C) (-3, -4). D) (-4, 5). Show Answer Correct Answer: C) (-3, -4). 31. The denotation used to indicate the distance from the center of the ellipse to the focus is ..... A) B. B) C. C) A. D) F. Show Answer Correct Answer: B) C. 32. What is the directrix of the parabola(x )$^{2 }$= 8y? A) Y=-2. B) Y= 2. C) X= 5. D) Y =-3. Show Answer Correct Answer: A) Y=-2. 33. What is the vertex of the parabola:$x=7\left(y-6\right)^2-2$ A) (-2, 6). B) (-2, -6). C) (-6, -2). D) (6, -2). Show Answer Correct Answer: A) (-2, 6). 34. What is the line containing the center and foci? A) Major Axis. B) Minor Axis. C) Vertices. D) None of the above. Show Answer Correct Answer: A) Major Axis. 35. Which of the following is the equation of an ellipse with center at $(0, 0)$ A) $\frac{x^2}{25} + \frac{y^2}{9} = 1$. B) $\frac{x^2}{25} + \frac{y^2}{16} = 1$. C) $\frac{x^2}{16} + \frac{y^2}{25} = 1$. D) $\frac{x^2}{9} + \frac{y^2}{25} = 1$. Show Answer Correct Answer: A) $\frac{x^2}{25} + \frac{y^2}{9} = 1$. 36. If a parabola has a vertex at (-5, 2), what is the axis of symmetry. A) X = 5. B) X =-5. C) Y =-2. D) Y = 2. Show Answer Correct Answer: B) X =-5. 37. What is the point inside the parabola 'p' units from the vertex? A) Directrix. B) Axis of symmetry. C) Vertex. D) Focus. Show Answer Correct Answer: D) Focus. 38. The equation that shows the relationship between the distances of the center the focus, vertex and covertex is ..... A) C$^{2}$ = a$^{2}$ + b$^{2}$. B) A$^{2}$ = b$^{2}$ + c$^{2}$. C) B$^{2}$ = a$^{2}$ + c$^{2}$. D) None of the above. Show Answer Correct Answer: B) A$^{2}$ = b$^{2}$ + c$^{2}$. 39. Which conic section is represented by the equationx$^{2}$ + y$^{2}$-10x-4y-21 = 0 A) Parabola. B) Circle. C) Ellipse. D) Hyperbola. Show Answer Correct Answer: B) Circle. 40. Write the equation of a circle in standard form:$8x+32y+y^2=-263-x^2$ A) $\left(x+4\right)^2+\left(y+16\right)^2=9$. B) (x+4)2+(y+16)2=9 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\left(x+4\right)^2+\left(y+16\right)^2=9$. 41. Which correctly describes the parabola:$y=2\left(x-1\right)^2-3$ A) Opens down. B) Opens right. C) Opens left. D) Opens up. Show Answer Correct Answer: D) Opens up. 42. What conic section is formed when the plane intersects only one cone to form a bounded curve or when the plane is tilted at any angle provided not parallel to the base, element or axis? A) Hyperbola. B) Circle. C) Ellipse. D) Parabola. Show Answer Correct Answer: C) Ellipse. 43. What best describe a HYPERBOLA? A) It is formed when the intersecting plane is parallel to the edge of the cone. B) It is formed when the intersecting plane is parallel to the base of the cone. C) It is formed when the intersecting plane is slightly tilted so as to make a closed figure. D) It is formed when the intersecting plane is positioned at a steeper angle. Show Answer Correct Answer: D) It is formed when the intersecting plane is positioned at a steeper angle. 44. What is the significance of the transverse axis in a hyperbola? A) It is the line segment that connects the vertices of the hyperbola and determines its orientation. B) It is the line that bisects the hyperbola into two equal parts. C) It represents the distance between the foci of the hyperbola. D) It is the axis that defines the asymptotes of the hyperbola. Show Answer Correct Answer: A) It is the line segment that connects the vertices of the hyperbola and determines its orientation. 45. These conics are formed when the cutting plane does not pass the vertex of the cone. These conics are also referred to as ..... A) Plane. B) Cone. C) Non-Degenerate Conics. D) Degenerate Conics. Show Answer Correct Answer: C) Non-Degenerate Conics. 46. Which of the following conic sections have four vertices? A) Circle. B) Ellipse. C) Hyperbola. D) Both Ellipse and Hyperbola. Show Answer Correct Answer: B) Ellipse. 47. Which conic section does the equation $r = \frac{6}{1-3\cos(\theta)}$ A) Ellipse. B) Circle. C) Parabola. D) Hyperbola. Show Answer Correct Answer: D) Hyperbola. 48. Which way does the parabola open? (y-4)$^{2 }$=-8(x+1) A) Left. B) Right. C) Up. D) Down. Show Answer Correct Answer: A) Left. 49. Identify the conic section described by the equation 2x$^{2}$-4y +3x-6 = 0. A) Hyperbola. B) Ellipse. C) Parabola. D) Circle. Show Answer Correct Answer: C) Parabola. 50. What happens to the parabola when you multiply its equation by a number less than 1? A) Graph moves DOWN. B) Graph moves UP. C) Graph gets WIDER. D) Graph gets NARROWER. Show Answer Correct Answer: C) Graph gets WIDER. 51. A CIRCLE IS A SPECIAL TYPE OF? A) ELLIPSE. B) PARABOLA. C) HYPERBOLA. D) CIRCLE. Show Answer Correct Answer: A) ELLIPSE. 52. Write an equation for an ellipse with the given characteristics:length of major axis = 12; foci at (-2, 1) (-2, -9) A) $\frac{\left(x-3\right)^2}{25}+\frac{\left(y+6\right)^2}{9}=1$. B) $\frac{\left(x+4\right)^2}{11}+\frac{\left(y+2\right)^2}{64}=1$. C) $\frac{\left(x+2\right)^2}{11}+\frac{\left(y+4\right)^2}{36}=1$. D) $\frac{\left(x-2\right)^2}{25}-\frac{\left(y+4\right)^2}{36}=1$. Show Answer Correct Answer: C) $\frac{\left(x+2\right)^2}{11}+\frac{\left(y+4\right)^2}{36}=1$. 53. Write the equation of a parabola with a vertex at (-2, 5), that opens down, and has a focal width of 12. A) $\left(x+2\right)^2=12\left(y-5\right)$. B) $\left(x-2\right)^2=-12\left(y+5\right)$. C) $\left(x-2\right)^2=12\left(y+5\right)$. D) $\left(x+2\right)^2=-12\left(y-5\right)$. Show Answer Correct Answer: D) $\left(x+2\right)^2=-12\left(y-5\right)$. 54. Write an equation for a parabola with the given focus F and vertex V:F(2, 5) V(-1, 5) A) $\left(x-5\right)^2=8\left(y+1\right)$. B) $\left(y-5\right)^2=-12\left(x+1\right)$. C) $\left(y-5\right)^2=12\left(x+1\right)$. D) $\left(y+5\right)^2=-12\left(x-1\right)$. Show Answer Correct Answer: C) $\left(y-5\right)^2=12\left(x+1\right)$. 55. The sum of the distances from the foci to any point on the ellipse is equivalent the length of the ..... A) Vertex. B) Minor axis. C) Covertex. D) Major axis. Show Answer Correct Answer: D) Major axis. 56. It is the distance from the center to any point of a circle. A) Directrix. B) Diameter. C) Focus. D) Radius. Show Answer Correct Answer: D) Radius. 57. State the turning point for the equation:y = (x-6)$^{2 }$-4 A) (-6, -4). B) (6, -4). C) (-6, 4). D) (6, 4). Show Answer Correct Answer: B) (6, -4). 58. Ellipses and hyperbolas have ..... directrices A) 2. B) 4. C) 3. D) 1. Show Answer Correct Answer: A) 2. 59. What best describe a LINE? A) It is formed when the intersecting plane is parallel to the edge of the cone. B) It is formed when the intersecting plane parallel to the base of the once intersects with its vertex. C) It is formed when the plane intersects the vertex of the cone and is tangent to it. D) It is formed when the plane passes through the vertex and through both cones. Show Answer Correct Answer: C) It is formed when the plane intersects the vertex of the cone and is tangent to it. 60. The endpoints of the radius of a circle is at (1, 2) and (4, 3). What is the equation that defines the circle if its center is at (4, 3)? A) $\left(x-3\right)^2+\left(y-4\right)^2=10$. B) $\left(x-3\right)^2+\left(y+4\right)^2=10$. C) $\left(x-4\right)^2+\left(y-3\right)^2=10$. D) $\left(x-4\right)^2+\left(y+3\right)^2=10$. Show Answer Correct Answer: A) $\left(x-3\right)^2+\left(y-4\right)^2=10$. ← PreviousNext →Related QuizzesScience QuizzesClass 11 QuizzesClass 11 Mathematics Chapter 11 Conic Sections Quiz 1Class 11 Mathematics Chapter 11 Conic Sections Quiz 2Class 11 Mathematics Chapter 11 Conic Sections Quiz 3Class 11 Mathematics Chapter 11 Conic Sections Quiz 4Class 11 Mathematics Chapter 11 Conic Sections Quiz 6Class 11 Mathematics Chapter 11 Conic Sections Quiz 7Class 11 Mathematics Chapter 11 Conic Sections Quiz 8Class 11 Mathematics Chapter 11 Conic Sections Quiz 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books