9000105503
Level:
B
Find the distance between the points where the
\(y\)-axis
intersects the following hyperbola.
\[
H\colon \frac{\left (x - 4\right )^{2}}
{8} -\frac{\left (y - 3\right )^{2}}
{1} = 1
\]
\(2\)
\(4\)
\(6\)
\(8\)
Conics
9000105504
Level:
B
Find the distance between the points where the
\(y\)-axis
intersects the following hyperbola.
\[
H\colon \frac{\left (x - 4\right )^{2}}
{10} -\frac{\left (y - 5\right )^{2}}
{15} = 1
\]
\(6\)
\(2\)
\(4\)
\(8\)
9000105505
Level:
B
Find the distance between the vertices of the following hyperbola.
\[
H\colon \frac{\left (x + 1\right )^{2}}
{25} -\frac{\left (y + 2\right )^{2}}
{16} = 1
\]
\(10\)
\(12\)
\(6\)
\(8\)
9000105506
Level:
B
Find the distance between the vertices of the following hyperbola.
\[
H\colon \frac{\left (x - 3\right )^{2}}
{16} -\frac{\left (y + 2\right )^{2}}
{25} = 1
\]
\(8\)
\(12\)
\(14\)
\(10\)
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.
\[
H\colon \frac{\left (x + 3\right )^{2}}
{9} -\frac{\left (y - 2\right )^{2}}
{27} = 1
\]
\(12\)
\(14\)
\(10\)
\(8\)
9000105509
Level:
B
Find the distance between the points of intersection of the given hyperbola with the given straight line.
\[
H\colon \frac{\left (x - 6\right )^{2}}
{10} -\frac{\left (y - 2\right )^{2}}
{6} = 1;\quad p\colon x - 11 = 0
\]
\(6\)
\(12\)
\(10\)
\(8\)
9000105510
Level:
B
Find the distance between the intersections of the following hyperbola and straight
line.
\[
H\colon \frac{\left (x - 2\right )^{2}}
{10} -\frac{\left (y + 2\right )^{2}}
{6} = 1;\quad p\colon y + 5 = 0
\]
\(10\)
\(12\)
\(6\)
\(8\)
9000120004
Level:
B
Find a conic section which allows to draw a line through the center of this conic and
this line does not have any common point with the conic.
hyperbola
circle
ellipse
parabola
no solution
9000120005
Level:
B
The executives of a camp organize a holiday game. For this game it is important
that the direct distance kitchen - tent - fireplace is equal for all tents in the camp.
Is this information enough to determine the curve passing through all the
tents in the camp? Is this curve a conic? If yes, determine which conic.
Yes, all the tents are on an ellipse.
Yes, all the tents are on a circle.
Yes, all the tents are on a parabola.
Yes, all the tents are on a hyperbola.
No, we do not have enough information to draw any conclusion.