Conics

9000168704

Level:

Given the ellipse

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

, find the vertex on the minor axis.

[- 4; 3]

[- 5; 3]

[- 2; 0]

[- 2; 1]

9000168705

Level:

Given the ellipse

16 x^{2} + 9 y^{2} + 32 x - 36 y - 92 = 0

, find the vertex on the major axis.

[- 1; - 2]

[- 1; - 1]

[3; 2]

[2; 2]

1003020404

Level:

The equation of a hyperbola is given by

9 x^{2} - 16 y^{2} - 108 x + 96 y + 36 = 0

. The length of its semi-major axis is:

4

16

3

9

25

1003020405

Level:

A hyperbola has two asymptotes with the equations

y = \frac{1}{3} (x + 2)

and

y = - \frac{1}{3} (x + 2)

. What are the coordinates of its centre?

[- 2; 0]

[2; 0]

[- \frac{1}{3}; 0]

[0; 2]

[\frac{1}{3}; 2]

1003020406

Level:

The equation of a hyperbola is given by

\frac{x^{2}}{4} - \frac{y^{2}}{3} = 1

. Which of the following are the asymptote equations of the hyperbola?

y = \pm \frac{\sqrt{3}}{2} x

x = \pm \frac{\sqrt{3}}{2} y

y = \pm \frac{3}{4} x

y = \pm \frac{4}{3} x

y = \pm \frac{2 \sqrt{3}}{3} x

1003020407

Level:

The equation of a hyperbola is given by

\frac{(x - 5)^{2}}{12} - \frac{(y + 3)^{2}}{8} = 1

. The centre of the hyperbola has the coordinates:

[5; - 3]

[- 5; 3]

[- 5; - 3]

[12; 8]

[8; 12]

1003020408

Level:

The equation of a hyperbola is given by

\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1

. What is the distance between its foci?

10

5

16

9

4

1003020409

Level:

The equation of a parabola is given by

y^{2} = 4 x

. What is the parameter value of this parabola?

2

4

\frac{1}{2}

\frac{1}{4}

1

1003020410

Level:

The equation of a parabola is given by

x^{2} + 4 y - 6 x + 3 = 0

. What is the parameter value of this parabola?

2

4

- 2

- 4

\frac{3}{2}

1003020411

Level:

A parabola has its focus

F = [5; 0]

and the directrix with the equation

x = 0

. What are the coordinates of its vertex?

[\frac{5}{2}; 0]

[0; 0]

[0; \frac{5}{2}]

[- 5; 0]

[- \frac{5}{2}; 0]

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