Gaokao Exam Analytic Geometry (Conic Sections) 1

Question 1

The equation of a circle is x² + y² - 6x + 8y - 11 = 0. What is the radius of this circle?

Accepted Answer

6

Answer

√56

Answer

6√2

Answer

√11

Question 2

A hyperbola has the equation x²/9 - y²/16 = 1. What are the coordinates of its foci?

Accepted Answer

(±5, 0)

Answer

(±3, 0)

Answer

(±4, 0)

Answer

(0, ±5)

Question 3

What is the directrix of the parabola x² = -12y?

Accepted Answer

y = 3

Answer

y = -3

Answer

x = 3

Answer

x = -3

Question 4

An ellipse has equation x²/16 + y²/7 = 1. What is its eccentricity?

Accepted Answer

3/4

Answer

√7/4

Answer

√7/3

Answer

3/7

Question 5

Which of the following points is on the parabola y² = 4x and is equidistant from the focus and the point (-3, 0)?

Accepted Answer

(1, -2)

Answer

(1, 2)

Answer

(4, 4)

Answer

(9, 6)

Question 6

Two foci of an ellipse are F₁(-√3, 0) and F₂(√3, 0), and the ellipse passes through the point (1, 1). What is the equation of the ellipse?

Accepted Answer

x²/4 + y²/1 = 1

Answer

x²/3 + y²/1 = 1

Answer

x²/4 + y²/3 = 1

Answer

x²/2 + y²/1 = 1