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2010006308

Level:

Find the equation of the circle, which passes through the points

A = [- 4; 2]

B = [1; 3]

and

C = [2; - 2]

(x + 1)^{2} + y^{2} = 13

(x - 1)^{2} + y^{2} = 13

x^{2} + (y - 1)^{2} = 13

x^{2} + y^{2} = 13 x

x^{2} + (y + 1)^{2} = 13

2010006006

Level:

Find the tangent equations from the point

M = [- 2; 2]

to the parabola given by

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

x - y + 4 = 0

x + y = 0

x + y - 4 = 0

x + y = 0

x + y + 4 = 0

x - y = 0

x - y - 4 = 0

x - y = 0

x + y - 4 = 0

x - y = 0

2010006005

Level:

Find the tangent equations from the point

N = [0; 0]

to the ellipse given by

2 x^{2} + y^{2} - 4 x - 8 y + 12 = 0

5 x + y = 0

x - y = 0

5 x - y = 0

x + y = 0

5 x - y = 0

x - y = 0

x + 5 y = 0

x - y = 0

x - 5 y = 0

x + y = 0

2010006004

Level:

The equation of a parabola is given by

x^{2} - 8 x + 3 y - 2 = 0

. Find the equation of a line, which passes through the vertex of this parabola and is parallel to the line

2 x - 5 y + 8 = 0

- 2 x + 5 y - 22 = 0

2 x - 5 y - 22 = 0

2 x - 5 y - 38 = 0

2 x - 5 y + 38 = 0

- 2 x + 5 y + 22 = 0

2010006003

Level:

Find the set of values of the parameter

c \in R

for which the line

5 x - 3 y - c = 0

isn't a secant of the ellipse

25 x^{2} + 16 y^{2} = 400

(- \infty; - 25] \cup [25; \infty)

(- 25; 25)

{- 25, 25}

(- \infty; - 25) \cup (25; \infty)

[25; \infty)

2010006002

Level:

Find the value of the parameter

p \in R

for which the line

2 x - y - 1 = 0

is a tangent of the parabola

x^{2} = 2 p y

\frac{1}{2}

- \frac{1}{2}

2

- 2

1

2010006001

Level:

Find the value of the parameter

r \in R

for which the line

2 x - y - 1 = 0

is a tangent of the hyperbola

2 x^{2} - y^{2} = r

1

- 1

2

- 3

3

2010005906

Level:

Find all the tangents to the hyperbola

y^{2} - 4 x^{2} = 12

such that the angle between each tangent and the

x

-axis is

45^{\circ}

y = x + 3, y = x - 3, y = - x + 3, y = - x - 3

y = x + 3, y = - x - 3

y = x + 3, y = x - 3

y = x + 3

2010005905

Level:

Find the tangent line

r

to the parabola

6 (x + 1) = (y - 3)^{2}

, so that the tangent

r

is parallel to the line

q : 3 x - 2 y + 7 = 0.

r : 3 x - 2 y + 11 = 0

r : 3 x - 2 y - 7 = 0

r : 3 x - 2 y - 13 = 0

r : 3 x - 2 y + 13 = 0

2010005904

Level:

Find a true statement about the ellipse

9 x^{2} + y^{2} + 18 x = 0.

The tangent to the ellipse can pass through any point on the line

x = 1

The tangent to the ellipse can pass through any point on the line

y = 1

The tangent to the ellipse can pass through the point

[- 1; 1]

The tangent to the ellipse can pass through any point on the line

y = - 1

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2010006308

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