Conic Sections

9000105407

Level:

Parabola is a set of points that are equidistant from the point (focus) and the line (directrix). Find the equation of the directrix of the parabola \(y^{2} + 6y - 12x + 21 = 0\).

\(x + 2 = 0\)

\(x - 5 = 0\)

\(y + 3 = 0\)

\(y - 1 = 0\)

9000105409

Level:

Find the distance between the point \([7;3]\) and the focus of the parabola \(x^{2} - 8x + 8y + 8 = 0\).

\(5\)

\(9\sqrt5\)

\(3\)

\(\sqrt{13}\)

9000097003

Level:

Consider the parabola \((x + 1)^{2} = 4(y - 3)\). Find the focus of this parabola.

\([-1;4]\)

\([-1;3]\)

\([3;-1]\)

\([0;3]\)

9000091203

Level:

Consider the circle \(x^{2} - 2x + y^{2} - 6y + 8 = 0\). Find the radius of the circle.

\(\sqrt{2}\)

\(2\)

\(3\)

\(4\)

9000097006

Level:

Consider the parabola \((y - 1)^{2} = 12(x - 1)\). Find the focus of this parabola.

\([4;1]\)

\([1;6]\)

\([3;1]\)

\([1;1]\)

9000097009

Level:

Consider the parabola \((y - 3)^{2} = -4(x + 2)\). Find the focus of this parabola

\([-3;3]\)

\([-2;3]\)

\([3;-2]\)

\([3;-4]\)

9000097001

Level:

Parabola is a set of the points that are equidistant from the point (focus) and the line (directrix). Find the directrix of the parabola \((x - 3)^{2} = 8y\).

\(y = -2\)

\(x = 3\)

\(x = 0\)

\(y = 0\)

9000097004

Level:

Parabola is a set of the points that are equidistant from the point (focus) and the line (directrix). Find the directrix of the parabola \((x + 2)^{2} = -8(y - 1)\).

\(y = 3\)

\(x = -2\)

\(x = 1\)

\(y = -4\)

9000097007

Level:

Parabola is a set of the points that are equidistant from the point (focus) and the line (directrix). Find the directrix of the parabola \((y - 4)^{2} = 8(x - 1)\).

\(x = -1\)

\(x = 4\)

\(y = 4\)

\(y = 2\)

9000097010

Level:

Parabola is a set of the points that are equidistant from the point (focus) and the line (directrix). Find the directrix of the parabola \((y + 3)^{2} = -8(x + 4)\).

\(x = -2\)

\(x = -4\)

\(y = -3\)

\(y = -2\)

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9000105409

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9000091203

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