9000105403
Level:
B
The parabola \(P\colon y^{2} + 2y + 10x - 24 = 0\) has
two \(y\)-intercepts.
Find their distance.
\(10\)
\(8\)
\(6\)
\(4\)
Conics
9000105404
Level:
B
The parabola \(P\colon y^{2} + 4y + 6x - 5 = 0\) has
two \(y\)-intercepts.
Find their distance.
\(6\)
\(8\)
\(10\)
\(4\)
9000105405
Level:
B
Parabola is a set of the points that are equidistant from the point (focus)
and the line (directrix). Find the equation of the directrix of the parabola
\(P\colon x^{2} - 4x - 6y - 17 = 0\).
\(y + 5 = 0\)
\(y - 3 = 0\)
\(x + 4 = 0\)
\(x - 2 = 0\)
9000105406
Level:
B
Parabola is a set of the points that are equidistant from the point (focus)
and the line (directrix). Find the equation of the directrix of the parabola
\(P\colon y^{2} + 4y + 4x - 4 = 0\).
\(x - 3 = 0\)
\(x + 4 = 0\)
\(y + 1 = 0\)
\(y - 2 = 0\)
9000105407
Level:
B
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
\(y^{2} + 6y - 12x + 21 = 0\).
\(x + 2 = 0\)
\(x - 5 = 0\)
\(y + 3 = 0\)
\(y - 1 = 0\)
9000105408
Level:
B
Parabola is a set of the points that are equidistant from the point (focus)
and the line (directrix). Find the equation of the directrix of the parabola
\(P\colon x^{2} - 8x + 6y + 19 = 0\).
\(y - 1 = 0\)
\(y + 2 = 0\)
\(x + 4 = 0\)
\(x - 3 = 0\)
9000105409
Level:
B
Find the distance between the point \([7;3]\)
and the focus of the parabola \(x^{2} - 8x + 8y + 8 = 0\).
\(5\)
\(9\sqrt5\)
\(3\)
\(\sqrt{13}\)
9000105410
Level:
B
Find the distance between the point \(X = [-3;-6]\)
and the focus of the parabola \(P\colon y^{2} + 2y - 24x + 73 = 0\).
\(13\)
\(12\)
\(5\)
\(1\)
9000105501
Level:
B
Find the distance between the points where the
\(x\)-axis
intersects the following hyperbola.
\[
H\colon \frac{\left (x - 3\right )^{2}}
{20} -\frac{\left (y - 2\right )^{2}}
{5} = 1
\]
\(12\)
\(14\)
\(10\)
\(8\)
9000105502
Level:
B
Find the distance between the points where the
\(x\)-axis
intersects the following hyperbola.
\[
H\colon \frac{\left (x - 1\right )^{2}}
{10} -\frac{\left (y - 3\right )^{2}}
{6} = 1
\]
\(10\)
\(14\)
\(12\)
\(8\)