Gaokao Exam Analytic Geometry (Conic Sections) 3

Question 1

A line y = kx + 1 is tangent to the parabola y² = 4x. What is the value of k?

Accepted Answer

1

Answer

2

Answer

1/2

Answer

-1

Question 2

The chord of contact of point P(2, 1) with respect to the circle x² + y² = 5 has equation:

Accepted Answer

2x + y = 5

Answer

x + 2y = 5

Answer

2x - y = 5

Answer

x - 2y = 5

Question 3

An ellipse has foci at F₁(-√3, 0) and F₂(√3, 0), and passes through point (1, 1). What is the sum of distances from (1,1) to the two foci?

Accepted Answer

4

Answer

2√2 + √2 = 4 (actually 2a)

Answer

2√3

Answer

2√5

Question 4

The directrix of the parabola x² = -12y is:

Accepted Answer

y = 3

Answer

y = -3

Answer

x = 3

Answer

x = -3

Question 5

Two circles x² + y² = 1 and x² + y² - 6x - 8y + 24 = 0 — what is their positional relationship?

Accepted Answer

Externally tangent

Answer

Internally tangent

Answer

Intersecting at two points

Answer

One inside the other without touching

Question 6

The eccentricity of the hyperbola x²/16 - y²/9 = 1 is:

Accepted Answer

5/4

Answer

4/5

Answer

√7/4

Answer

5/3