FREE Gaokao Analytic Geometry (Conic Sections) Questions and Answers

Question 1

An ellipse has foci at F1(-1, 0) and F2(1, 0). The perimeter of a triangle formed by a point P on the ellipse and the two foci is 10. What is the standard equation of the ellipse?

Accepted Answer

x²/16 + y²/15 = 1

Answer

x²/25 + y²/24 = 1

Answer

x²/10 + y²/9 = 1

Answer

x²/16 + y²/17 = 1

Question 2

The line y = kx + 1 intersects the parabola y² = 4x at exactly one point. What is the value of k (where k ≠ 0)?

Accepted Answer

k = 1

Answer

k = 2

Answer

k = -1

Answer

k = 1/2

Question 3

What are the equations of the asymptotes for the hyperbola x²/9 - y²/16 = 1?

Accepted Answer

y = ±(4/3)x

Answer

y = ±(3/4)x

Answer

y = ±(9/16)x

Answer

y = ±(16/9)x

Question 4

The distance between the two foci of an ellipse is 8, and its eccentricity is 4/5. What is the length of the major axis?

Accepted Answer

10

Answer

5

Answer

8

Answer

12.5

Question 5

A point M is on the parabola x² = 8y. If the distance from M to the x-axis is 5, what is the distance from M to the focus F of the parabola?

Accepted Answer

7

Answer

3

Answer

5

Answer

8

Question 6

A hyperbola has the equation x²/a² - y²/12 = 1. If one of its foci is at (4, 0), what is the value of a?

Accepted Answer

2

Answer

4

Answer

√28

Answer

16

An ellipse has foci at F1(-1, 0) and F2(1, 0).The perimeter of a triangle formed by a point P on the ellipse and the two foci is 10.What is the standard equation of the ellipse?

An ellipse has foci at F1(-1, 0) and F2(1, 0).
The perimeter of a triangle formed by a point P on the ellipse and the two foci is 10.
What is the standard equation of the ellipse?