Conics

Parabola and Its Equation II

Submitted by vladimir.arzt on Sun, 03/17/2024 - 14:57

Submitted by vladimir.arzt on Sun, 03/17/2024 - 11:43

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Submitted by vladimir.arzt on Sat, 03/02/2024 - 15:16

Level:

Find the points of intersection of the circle

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

and the line

x - y + 4 = 0

[- 4; 0]

[0; 4]

[0; - 4]

[- 4; 0]

[4; 0]

[0; 4]

[- 4; 0]

[4; 0]

[4; 0]

[0; - 4]

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

Level:

The equation of a parabola is given by

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

. Find the equation of its directrix.

x = \frac{31}{16}

x = - \frac{33}{16}

x = \frac{33}{16}

x = - \frac{31}{16}

x = \frac{15}{8}

Level:

The equation of a hyperbola with the center

S = [1; - 3]

, the focus

F = [1; 2]

, and the vertex

A = [1; 0]

is given by:

\frac{(y + 3)^{2}}{9} - \frac{(x - 1)^{2}}{16} = 1

\frac{(x - 1)^{2}}{16} - \frac{(y + 3)^{2}}{9} = 1

\frac{(x - 1)^{2}}{9} - \frac{(y + 3)^{2}}{16} = 1

\frac{(y + 3)^{2}}{16} - \frac{(x - 1)^{2}}{9} = 1

\frac{(x + 1)^{2}}{16} - \frac{(y - 3)^{2}}{9} = 1