9000105506
Level:
B
Find the distance between the vertices of the following hyperbola.
\[
H\colon \frac{\left (x - 3\right )^{2}}
{16} -\frac{\left (y + 2\right )^{2}}
{25} = 1
\]
\(8\)
\(12\)
\(14\)
\(10\)
B
9000105507
Level:
B
Find the distance between the foci of the following hyperbola.
\[
H\colon \frac{\left (x + 1\right )^{2}}
{16} -\frac{\left (y + 5\right )^{2}}
{9} = 1
\]
\(10\)
\(12\)
\(8\)
\(6\)
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.
\[
H\colon \frac{\left (x - 4\right )^{2}}
{8} -\frac{\left (y - 3\right )^{2}}
{1} = 1
\]
\(2\)
\(4\)
\(6\)
\(8\)
9000106304
Level:
B
Find the third coordinate of the point
\(B = [2;0;?]\) using the fact that this
point is in the plane \(\alpha \)
defined by the equation
\[
\alpha \colon 2x + y - z - 5 = 0.
\]
Use the point \(B\) to
find the angle \(\varphi \)
between the plane \(\alpha \)
and the line \(AB\),
where \(A = [0;0;1]\).
\(\varphi = 60^{\circ }\)
\(\varphi = 45^{\circ }\)
\(\varphi = 30^{\circ }\)
\(\varphi = 75^{\circ }\)
9000106306
Level:
B
Find the general equation of the plane which is perpendicular to the plane
\(\alpha \)
\[
\alpha \colon 2x + y - z - 5 = 0
\]
and contains the line \(AB\),
where \(A = [0;0;1]\)
and \(B\) is a
point in \(\alpha \)
defined by it's first two coordinates
\[
B = [2;0;?].
\]
\(x - y + z - 1 = 0\)
\(x + y - z + 1 = 0\)
\(2x - y + z - 1 = 0\)
\(- 2x + y - z + 1 = 0\)