9000105507
Level:
B
Find the distance between the foci of the following hyperbola.
\[
H\colon \frac{\left (x + 1\right )^{2}}
{16} -\frac{\left (y + 5\right )^{2}}
{9} = 1
\]
\(10\)
\(12\)
\(8\)
\(6\)
Conics
9000105508
Level:
B
Find the distance between the foci of the following hyperbola.
\[
H\colon \frac{\left (x + 3\right )^{2}}
{9} -\frac{\left (y - 2\right )^{2}}
{27} = 1
\]
\(12\)
\(14\)
\(10\)
\(8\)
9000105510
Level:
B
Find the distance between the intersections of the following hyperbola and straight
line.
\[
H\colon \frac{\left (x - 2\right )^{2}}
{10} -\frac{\left (y + 2\right )^{2}}
{6} = 1;\quad p\colon y + 5 = 0
\]
\(10\)
\(12\)
\(6\)
\(8\)
9000105410
Level:
B
Find the distance between the point \(X = [-3;-6]\)
and the focus of the parabola \(P\colon y^{2} + 2y - 24x + 73 = 0\).
\(13\)
\(12\)
\(5\)
\(1\)
9000105504
Level:
B
Find the distance between the points where the
\(y\)-axis
intersects the following hyperbola.
\[
H\colon \frac{\left (x - 4\right )^{2}}
{10} -\frac{\left (y - 5\right )^{2}}
{15} = 1
\]
\(6\)
\(2\)
\(4\)
\(8\)
9000105502
Level:
B
Find the distance between the points where the
\(x\)-axis
intersects the following hyperbola.
\[
H\colon \frac{\left (x - 1\right )^{2}}
{10} -\frac{\left (y - 3\right )^{2}}
{6} = 1
\]
\(10\)
\(14\)
\(12\)
\(8\)
9000105503
Level:
B
Find the distance between the points where the
\(y\)-axis
intersects the following hyperbola.
\[
H\colon \frac{\left (x - 4\right )^{2}}
{8} -\frac{\left (y - 3\right )^{2}}
{1} = 1
\]
\(2\)
\(4\)
\(6\)
\(8\)
9000105501
Level:
B
Find the distance between the points where the
\(x\)-axis
intersects the following hyperbola.
\[
H\colon \frac{\left (x - 3\right )^{2}}
{20} -\frac{\left (y - 2\right )^{2}}
{5} = 1
\]
\(12\)
\(14\)
\(10\)
\(8\)
9000105509
Level:
B
Find the distance between the points of intersection of the given hyperbola with the given straight line.
\[
H\colon \frac{\left (x - 6\right )^{2}}
{10} -\frac{\left (y - 2\right )^{2}}
{6} = 1;\quad p\colon x - 11 = 0
\]
\(6\)
\(12\)
\(10\)
\(8\)
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
\(P\colon x^{2} - 8x + 6y + 19 = 0\).
\(y - 1 = 0\)
\(y + 2 = 0\)
\(x + 4 = 0\)
\(x - 3 = 0\)