Gaokao Exam Analytic Geometry (Conic Sections) 2

Question 1

The equation of an ellipse is x²/25 + y²/16 = 1. What is the distance between its two foci?

Accepted Answer

6

Answer

8

Answer

10

Answer

3

Question 2

A parabola has the equation y² = 8x. What are the coordinates of its focus?

Accepted Answer

(2, 0)

Answer

(0, 2)

Answer

(4, 0)

Answer

(-2, 0)

Question 3

Which of the following is the equation of a hyperbola with real axis along the y-axis?

Accepted Answer

y²/9 - x²/4 = 1

Answer

x²/9 - y²/4 = 1

Answer

x²/4 + y²/9 = 1

Answer

y²/9 + x²/4 = 1

Question 4

If the eccentricity of an ellipse is 1/2, and one semi-axis is a = 4, what is the length of the other semi-axis b?

Accepted Answer

2√3

Answer

2

Answer

√15

Answer

3

Question 5

A circle passes through the origin and has center at (3, 4). What is the equation of this circle?

Accepted Answer

(x-3)² + (y-4)² = 25

Answer

(x-3)² + (y-4)² = 5

Answer

x² + y² = 25

Answer

(x+3)² + (y+4)² = 25

Question 6

The asymptotes of the hyperbola x²/4 - y²/9 = 1 are:

Accepted Answer

y = ±(3/2)x

Answer

y = ±(2/3)x

Answer

y = ±(4/9)x

Answer

y = ±2x