Conics

1003020403

Level:

An ellipse has the centre at

S = [- 1; 3]

, the semi major axis with the length of

3

and the semi minor axis with the length of

2

. The semi major axis is parallel to

y

axis. The equation of the ellipse is:

\frac{(x + 1)^{2}}{4} + \frac{(y - 3)^{2}}{9} = 1

\frac{(x + 1)^{2}}{9} + \frac{(y - 3)^{2}}{4} = 1

\frac{(x - 1)^{2}}{4} + \frac{(y + 3)^{2}}{9} = 1

\frac{(x + 1)^{2}}{4} - \frac{(y - 3)^{2}}{9} = 1

\frac{(x + 1)^{2}}{4} + \frac{(y - 3)^{2}}{9} = - 1

1003020402

Level:

The equation of an ellipse is given by

x^{2} + 4 y^{2} - 6 x + 32 y + 48 = 0

. The length of its semi-minor axis is:

\frac{5}{2}

5

25

\frac{25}{4}

\frac{15}{2}

1003020401

Level:

The equation of an ellipse is given by

5 x^{2} + 9 y^{2} - 30 x - 18 y + 9 = 0

. The length of its semi-major axis is:

3

5

9

\sqrt{5}

14

9000168710

Level:

Find the vertex of the hyperbola

9 x^{2} - 25 y^{2} + 18 x + 100 y - 316 = 0

[4; 2]

[2; 2]

[- 1; - 3]

[- 1; - 1]

9000168709

Level:

Find the vertex of the hyperbola

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

[2; - 6]

[2; - 7]

[5; - 3]

[6; - 3]

9000168702

Level:

Given the ellipse

4 x^{2} + 9 y^{2} + 16 x - 18 y - 11 = 0

, find the coordinates of the vertex on the minor axis.

[- 2; 3]

[- 2; 4]

[0; 1]

[1; 1]

9000168708

Level:

Find the vertex of the hyperbola

4 x^{2} - 9 y^{2} + 24 x + 18 y + 63 = 0

[- 3; 3]

[- 3; 4]

[- 6; 1]

[- 5; 1]

9000168703

Level:

Given the ellipse

25 x^{2} + 9 y^{2} - 150 x + 18 y + 9 = 0

, find the vertex on the major axis.

[3; 4]

[3; 2]

[8; - 1]

[6; - 1]

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]

1003020403

1003020402

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