9000105507
Level:
B
Find the distance between the foci of the following hyperbola.
\[
H\colon \frac{\left (x + 1\right )^{2}}
{16} -\frac{\left (y + 5\right )^{2}}
{9} = 1
\]
\(10\)
\(12\)
\(8\)
\(6\)
B
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 \(P\colon y^{2} + 2y - 24x + 73 = 0\).
\(13\)
\(12\)
\(5\)
\(1\)
9000101904
Level:
B
Find the angle between the \(x\)-axis
and the line \(p\).
\[
\begin{aligned}p\colon x& = 2 - t, &
\\y & = 3t,
\\z & = 1;\ t\in \mathbb{R}
\\ \end{aligned}
\]
Round your answer to the nearest minute.
\(71^{\circ }34'\)
\(0^{\circ }\)
\(69^{\circ }17'\)
\(90^{\circ }\)
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
\(P\colon y^{2} + 4y + 4x - 4 = 0\).
\(x - 3 = 0\)
\(x + 4 = 0\)
\(y + 1 = 0\)
\(y - 2 = 0\)
9000101905
Level:
B
The points \(A = [0;5;0]\),
\(B = [5;5;0]\),
\(C = [5;0;0]\),
\(D = [0;0;0]\) define the cube
\(ABCDEFGH\). Find the angle
between the lines \(BF\)
and \(AC\).
Round your answer to the nearest minute.
\(90^{\circ }\)
\(0^{\circ }\)
\(45^{\circ }\)
\(73^{\circ }47'\)
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
\(P\colon x^{2} - 8x + 6y + 19 = 0\).
\(y - 1 = 0\)
\(y + 2 = 0\)
\(x + 4 = 0\)
\(x - 3 = 0\)
9000101906
Level:
B
Find the angle between the planes \(\alpha \)
and \(\beta \).
\[
\alpha \colon 2x - 5y + 3z - 4 = 0,\qquad \beta \colon x - 3 = 0
\]
Round your answer to the nearest minute.
\(71^{\circ }4'\)
\(21^{\circ }42'\)
\(82^{\circ }19'\)
\(85^{\circ }2'\)
9000101907
Level:
B
The general plane \(\alpha \)
has the equation
\[
\alpha \colon 3z - 4 = 0
\]
and the plane \(\beta \) has a
normal vector \(\vec{n} = (0;0;1)\). Find
the angle between \(\alpha \)
and \(\beta \)
and round your answer to the nearest degree.
\(0^{\circ }\)
\(30^{\circ }\)
\(45^{\circ }\)
\(90^{\circ }\)