Conics

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

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}

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

1003024002

Level:

The equation of an ellipse is given by

\frac{x^{2}}{48} + \frac{y^{2}}{36} = 1

. The point

[- 2; 5]

represents:

a point inside the ellipse

vertex of the ellipse

co-vertex of the ellipse

a point outside the ellipse

the centre of the ellipse

1103040101

Level:

The equation of an ellipse is given by

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

. Which of the pictures below shows the given ellipse in the rectangular coordinate system?

1103040102

Level:

The diagram of an ellipse in the rectangular coordinate system is shown in the picture. Find the standard form equation of this ellipse:

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

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

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

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

1103040103

Level:

The diagram of an ellipse in the rectangular coordinate system is shown in the picture.What is the semi-major axis of this ellipse?

The segment

S N

The segment

S K

The line

E F

The line

K L

1103040106

Level:

A circle in the rectangular coordinate system is shown in the picture. What is the standard form equation of this circle?

x^{2} + (y - 3)^{2} = 4

x^{2} + (y + 3)^{2} = 4

x^{2} + (y - 3)^{2} = 2

x^{2} + (y + 3)^{2} = 2

1103040107

Level:

The picture below shows an ellipse drawn in the rectangular coordinate system. What is the semi-minor axis of this ellipse?

The segment

S M

The segment

S L

The line

M N

The line

E F

2010005908

Level:

Which of the given points is one of the co-vertices on the minor axis of the ellipse

25 x^{2} + 9 y^{2} + 100 x - 54 y - 44 = 0

[- 5; 3]

[- 2; 0]

[- 2; - 2]

[3; 1]

1003020401

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2010005908

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