This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 11 Conic Sections – Quiz 6 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 11 Conic Sections Quiz 6 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Identify the conic section described by the equation 6x$^{2}$ + 6y$^{2}$-3x + 4y = 0. A) Ellipse. B) Hyperbola. C) Circle. D) Parabola. Show Answer Correct Answer: C) Circle. 2. The parabola y = 1/2 (x + 4)$^{2}$-3 will A) Open down. B) Open up. C) All the above. D) None of the above. Show Answer Correct Answer: B) Open up. 3. Write an equation for an ellipse with the given characteristics:vertices at (7, -4) (-3, -4); foci at (6, -4) (-2, -4) A) $\frac{\left(x+2\right)^2}{9}+\frac{\left(y+4\right)^2}{25}=1$. B) $\frac{\left(x-2\right)^2}{16}+\frac{\left(y-4\right)^2}{9}=1$. C) $\frac{\left(x-2\right)^2}{25}+\frac{\left(y+4\right)^2}{9}=1$. D) $\frac{\left(x-2\right)^2}{25}-\frac{\left(y+4\right)^2}{9}=1$. Show Answer Correct Answer: C) $\frac{\left(x-2\right)^2}{25}+\frac{\left(y+4\right)^2}{9}=1$. 4. Identify the given conic sections that the equation represents. $x^2+16y+6x=y^2+119$ A) Parabola. B) Hyperbola. C) Ellipse. D) Circle. Show Answer Correct Answer: B) Hyperbola. 5. A hyperbola is formed if the angle of the cutting plane with the vertical axis is greater than the vertex angle. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 6. Identify the eccentricity of the conic section given by the polar equation $r = \frac{3}{1 + 2\sin(\theta)}$ A) 1.5. B) 0.5. C) 1. D) 2. Show Answer Correct Answer: D) 2. 7. Find the foci of the hyperbola given by the equation $\frac{x^2}{36}-\frac{y^2}{16} = 1$ A) $(\pm \sqrt{52}, 0)$. B) $(0, \pm \sqrt{52})$. C) $(\pm \sqrt{20}, 0)$. D) $(0, \pm \sqrt{20})$. Show Answer Correct Answer: A) $(\pm \sqrt{52}, 0)$. 8. Find the length of the transverse axis of a hyperbola with eccentricity 2 and distance between foci is $4\sqrt{2}$ A) $\frac{4}{3}\sqrt{2}$. B) 3. C) $\frac{2}{3}\sqrt{2}$. D) 4. Show Answer Correct Answer: C) $\frac{2}{3}\sqrt{2}$. 9. The distance between the foci of a hyperbola is 16 and its eccentricity is 2 . Its equation is A) X$^{2}$-y$^{2}$ = 32. B) X$^{2}$ + y$^{2}$ = 32. C) 2x$^{2}$-y$^{2}$ = 7. D) None of these. Show Answer Correct Answer: A) X$^{2}$-y$^{2}$ = 32. 10. TRUE or FALSE:A circle is a special type of ellipse. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 11. Which one is the equation of the directrix of the parabolax$^{2 }$= 8y? A) Y = 2. B) Y =-2. C) X = 2. D) X =-2. Show Answer Correct Answer: B) Y =-2. 12. Is the locus of a point which moves so that the difference of its distances from two fixed points is constant. A) Hyperbola. B) Ellipse. C) Parabola. D) Circle. Show Answer Correct Answer: A) Hyperbola. 13. What type of conic section is this equation? $\frac{\left(x+2\right)^2}{9}+\frac{\left(y-4\right)^2}{25}=1$ A) Circle. B) Ellipse. C) Hyperbola. D) Parabola. Show Answer Correct Answer: B) Ellipse. 14. Which of the following equations represent a hyperbola? A) $4x^2+8y^2+16x-16y-20=0$. B) $4x^2-4y^2+16x-16y-20=0$. C) $4x^2+4y^2+16x-16y-20=0$. D) $4x^2+16x-16y-20=0$. Show Answer Correct Answer: B) $4x^2-4y^2+16x-16y-20=0$. 15. What is the focus of a parabola? A) A point from which distances to points on the parabola are measured, lying on the axis of symmetry. B) The vertex of the parabola where it changes direction. C) A line that runs parallel to the directrix of the parabola. D) The endpoint of the latus rectum of the parabola. Show Answer Correct Answer: A) A point from which distances to points on the parabola are measured, lying on the axis of symmetry. 16. Identify the conic represented by the equation without completing the square:$x^2+16y^2-160y+384=0$ A) Hyperbola. B) Cirlce. C) Parabola. D) Ellipse. Show Answer Correct Answer: D) Ellipse. 17. Identify the conic section $\left(y-9\right)^2=\left(x+4\right)$ A) Hyperbola. B) Ellipse. C) Circle. D) Parabola. Show Answer Correct Answer: D) Parabola. 18. Write the equation of a circle with a center at (2, -3) and a radius of 4. A) $\left(x+2\right)^2+\left(y-3\right)^2=4$. B) $\left(x+2\right)^2+\left(y-3\right)^2=16$. C) $\left(x-2\right)^2+\left(y-3\right)^2=4$. D) $\left(x-2\right)^2+\left(y+3\right)^2=16$. Show Answer Correct Answer: D) $\left(x-2\right)^2+\left(y+3\right)^2=16$. 19. What is formed when the plane intersects the cones at the vertex only? A) A point. B) A single line. C) Intersecting lines. D) Degenerate conics. Show Answer Correct Answer: A) A point. 20. The standard formula for a circle. A) $\left(x+h\right)^2-\left(y+k\right)^2=r^2$. B) $x^2-y^2+Dx+Ey+F=0$. C) $x^2+y^2+Dx+Ey+F=0$. D) $\left(x-h\right)^2+\left(y-k\right)^2=r^2$. Show Answer Correct Answer: D) $\left(x-h\right)^2+\left(y-k\right)^2=r^2$. 21. Identify the conic:6x$^{2}$ + 6y$^{2}$-3x + 4y = 0 A) Ellipse. B) Parabola. C) Hyperbola. D) Circle. Show Answer Correct Answer: D) Circle. 22. Identify the given conic sections that the equation represents. $16x^2+25y^2-64x-336=0$ A) Ellipse. B) Circle. C) Hyperbola. D) Parabola. Show Answer Correct Answer: A) Ellipse. 23. Identify the given conic sections that the equation represents. $4x^2+4y^2-20x-32y+81=0$ A) Ellipse. B) Parabola. C) Circle. D) Hyperbola. Show Answer Correct Answer: C) Circle. 24. All radii of a circle have equal length. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 25. How do you graph a circle given its equation in standard form? A) Connect the points on the graph to form a circle. B) Plot the center and use the radius to plot points around it to form the circle. C) Use the equation to find the slope and intercept. D) Graph the equation as a straight line. Show Answer Correct Answer: B) Plot the center and use the radius to plot points around it to form the circle. 26. Which of the following is the equation for a circle with a center at (-8, -3) and a radius of 4? A) (x-8)$^{2}$ + (y-3)$^{2}$ = 16. B) (x-8)$^{2}$ + (y+3)$^{2}$ = 4. C) (x+8)$^{2}$ + (y+3)$^{2}$ = 16. D) (x+8)$^{2}$ + (y-3)$^{2}$ = 4. Show Answer Correct Answer: C) (x+8)$^{2}$ + (y+3)$^{2}$ = 16. 27. Find the vertices:$\frac{\left(x-1\right)^2}{4}-\frac{\left(y+2\right)^2}{1}=1$ A) (3, -2) and (-1, -2). B) (1, 2) and (-1, 2). C) (1, 0) and (1, -4). D) (-1, 0) and (-1, 4). Show Answer Correct Answer: A) (3, -2) and (-1, -2). 28. What is the orientation of this ellipse? A) Horizontal. B) Vertical. C) All the above. D) None of the above. Show Answer Correct Answer: B) Vertical. 29. What is the center for the following equation? $\frac{\left(y+2\right)^2}{9}-\frac{\left(x-4\right)^2}{25}=1$ A) (2, -4). B) (-4, -2). C) (-2, 4). D) (4, -2). Show Answer Correct Answer: D) (4, -2). 30. What is the vertex of the parabola:y=2(x-3)$^{2}$+4 A) (3, -4). B) (-3, 4). C) (-3, -4). D) (3, 4). Show Answer Correct Answer: D) (3, 4). 31. A degenerate ellipse is represented by a line. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 32. Write an equation for the ellipse with each set of characteristics. Vertices ( 4, 3), (4, -9). Length of minor axis is 8 A) $\frac{\left(x-4\right)^2}{16}+\frac{\left(y+3\right)^2}{36}=1$. B) 16(x-4)2+36(y+3)2=1 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\frac{\left(x-4\right)^2}{16}+\frac{\left(y+3\right)^2}{36}=1$. 33. Identify the conic represented by the equation without completing the square:$x^2+y^2+3x-2y-1=0$ A) Hyperbola. B) Parabola. C) Ellipse. D) Cirlce. Show Answer Correct Answer: D) Cirlce. 34. What is the equation of the circle that passes through (-15, 10) and has a center at (-16, 11)? A) $\left(x+16\right)^2+\left(y-11\right)^2=2$. B) $\left(x+11\right)^2+\left(y-16\right)^2=4$. C) $\left(x+13\right)^2+\left(y-17\right)^2=2$. D) $\left(x+16\right)^2+\left(y-11\right)^2=4$. Show Answer Correct Answer: A) $\left(x+16\right)^2+\left(y-11\right)^2=2$. 35. Which shape graph would the equation make? $x^2+y^2-2x+5x-19=0$ A) Hyperbola. B) Ellipse. C) Parabola. D) Circle. Show Answer Correct Answer: D) Circle. 36. Conics is the intersection of a plane and the right circular cones called nappes. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 37. When the plane is perpendicular to the axis the ellipse become a ..... A) TRIANGLE. B) LINE. C) POINT. D) CIRCLE. Show Answer Correct Answer: D) CIRCLE. 38. Identify the conic:2x$^{2}$ + 6y-9 = 0 A) Circle. B) Parabola. C) Hyperbola. D) Ellipse. Show Answer Correct Answer: B) Parabola. 39. Identify the given conic sections that the equation represents. $x^2+y^2+6x-2y+9=0$ A) Circle. B) Ellipse. C) Hyperbola. D) Parabola. Show Answer Correct Answer: A) Circle. 40. The equation of an ellipse centered at (3, 2) with a vertical major axis of length 8 and a minor axis of length 4 is A) $\frac{\left(x-3\right)^2}{16}+\frac{\left(y-2\right)^2}{64}=1$. B) $\frac{\left(x-3\right)^2}{64}+\frac{\left(y-2\right)^2}{16}=1$. C) $\frac{\left(x-3\right)^2}{4}+\frac{\left(y-2\right)^2}{16}=1$. D) $\frac{\left(x-3\right)^2}{16}+\frac{\left(y-2\right)^2}{4}=1$. Show Answer Correct Answer: C) $\frac{\left(x-3\right)^2}{4}+\frac{\left(y-2\right)^2}{16}=1$. 41. The equation of the circle which passes through the point (4, 5) and has its centre at (2, 2) is A) $\left(x-4\right)^2+\left(y-5\right)^2=14$. B) $\left(x+2\right)^2+\left(y-3\right)^2=5$. C) $\left(x-2\right)^2-\left(y-2\right)^2=13$. D) $\left(x-2\right)^2+\left(y-2\right)^2=13$. Show Answer Correct Answer: D) $\left(x-2\right)^2+\left(y-2\right)^2=13$. 42. If the directrix is y = 4 and the focus is at (3, 0), the value of p is: A) 2. B) -8. C) 8. D) -2. Show Answer Correct Answer: D) -2. 43. If the cutting plane passes through the vertex perpendicular to the cone axis, a point is formed. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 44. Graph the hyperbola given by the equation $\frac{(y-3)^2}{4}-\frac{(x+1)^2}{9} = 1$ A) $(-1, 3)$ $(-1, 3)$. B) $(-1, 5)$ $(-1, 1)$. C) $(-1, 5)$ $(-1, 1)$. D) $(0, 3)$ $(6, 3)$. Show Answer Correct Answer: B) $(-1, 5)$ $(-1, 1)$. 45. It is a curve where any point is at an equal distance from a fixed point (the focus ) and a fixed line (directrix). A) Circle. B) Parabola. C) Hyperbola. D) Ellipse. Show Answer Correct Answer: B) Parabola. 46. X$^{2}$$^{}$-y $^{2}$ = 8 A) Ellipse. B) Parabola. C) Circle. D) Hyperbola. Show Answer Correct Answer: D) Hyperbola. 47. These are figures that formed by intersecting two inverted cones and a plane. A) Cross Sections. B) Circles. C) Parabolas. D) Conic Sections. Show Answer Correct Answer: D) Conic Sections. 48. In the equation (x-4)$^{2}$+(x-3)$^{2}$=25, the radius is A) 3. B) 5. C) 4. D) 25. Show Answer Correct Answer: B) 5. 49. What is the coordinates of the centre and the radius of the circle with equation:(x + 2)$^{2}$ + (y + 5)$^{2}$ = 16? A) Centre (-2, -5)r = 16 units. B) Centre (2, 5)Radius = 16 units. C) Centre (2, 5)Radius = 4 units. D) Centre (-2, -5)Radius = 4 units. Show Answer Correct Answer: D) Centre (-2, -5)Radius = 4 units. 50. By inspection, identify the type of conic section generated by the equation:$-25x^2+y^2-100x-125=0$ A) Circle. B) Hyperbola. C) Parabola. D) Ellipse. Show Answer Correct Answer: B) Hyperbola. 51. Given the equation 3x$^{2 }$-7y$^{2 }$+ 12x + 14y + 13 = 0, what type of conic section is this? A) Ellipse. B) Circle. C) Hyperbola. D) Parabola. Show Answer Correct Answer: C) Hyperbola. 52. Write the equations of the asymptotes for the hyperbola $\frac{\left(y+2\right)^2}{36}-x^2=1$ A) $y+2=\pm6\left(x-1\right)$. B) $y-1=\pm6\left(x-2\right)$. C) $y=\pm6x$. D) $y+2=\pm6x$. Show Answer Correct Answer: D) $y+2=\pm6x$. 53. In the equation (x+2)$^{2}$+(y+3)$^{2}$=49, what is the center of the circle? A) (2, 3). B) (-3, -2). C) (-2, -3). D) (3, 2). Show Answer Correct Answer: C) (-2, -3). 54. An ellipse degenerates into a circle if A) C=0. B) C=a. C) All the above. D) None of the above. Show Answer Correct Answer: A) C=0. 55. What is the center of this circle:$x^2+y^2-10y+16=0$ A) ( 0, 4 ). B) ( 0, 7 ). C) ( 0, 6 ). D) ( 0, 5 ). Show Answer Correct Answer: D) ( 0, 5 ). 56. The major axis is: A) The closest point closest to the Sun. B) The shorter axis of an ellipse. C) The longer axis of an ellipse. D) The farthest point closest to the Sun. Show Answer Correct Answer: C) The longer axis of an ellipse. 57. What best describe a PARABOLA? 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: A) It is formed when the intersecting plane is parallel to the edge of the cone. 58. When a plane intersects a double right circular cone, two dimensional curves called conic sections are formed. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 59. What is the center of this circle:$x^2+y^2-4x-6y-3=0$ A) ( 2, 3 ). B) ( 2, -3 ). C) (-2, 3 ). D) ( 3, 2 ). Show Answer Correct Answer: C) (-2, 3 ). 60. Identify the conic:36x$^{2}$-5y$^{2}$ + 8x + 2y + 12 = 0 A) Ellipse. B) Circle. C) Hyperbola. D) Parabola. Show Answer Correct Answer: C) Hyperbola. ← 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 5Class 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