1003024102
Level:
B
The equation of a parabola is given by \( 3y^2+x-12y+14=0 \). Find the equation of its directrix.
\( x=-\frac{23}{12} \)
\( x=\frac{23}{12} \)
\( y=-\frac{23}{12} \)
\( y=\frac{23}{12} \)
\( x=-\frac{11}{6} \)
Conics
1103040104
Level:
B
The picture shows a hyperbola drawn in the rectangular coordinate system. What is the eccentricity of this hyperbola?
The distance of points \( S \) and \( F \)
The distance of points \( S \) and \( A \)
The distance of points \( A \) and \( B \)
The distance of points \( E \) and \( F \)
1103040105
Level:
B
A parabola is given by the picture. What is the parameter of this parabola?
The distance of the point \( F \) from the line \( d \)
The distance of points \( V \) and \( F \)
A half of the segment \( DV \)
Two times the distance of the point \( F \) from the line \( d \)
1103040108
Level:
B
A parabola in the rectangular coordinate system is shown in the picture. What is the vertex form equation of this parabola?
\( x^2 = 4(y-1) \)
\( x^2 = 4(y+1) \)
\( y^2 = 4(x-1) \)
\( y^2 = 4(x+1) \)
1103040109
Level:
B
The picture shows a hyperbola drawn in the rectangular coordinate system. What is the minor axis of this hyperbola?
The \( y \)-axis
The segment \( EF \)
The \( x \)-axis
The segment \( AB \)
1103040110
Level:
B
The picture shows a hyperbola drawn in the rectangular coordinate system. What is the major axis of this hyperbola?
The \( y \)-axis
The segment \( AB \)
The segment \( EF \)
The \( x \)-axis
2010005901
Level:
B
Find the distance between the points where the
\(y\)-axis
intersects the following hyperbola.
\[
H\colon \frac{\left (y+3\right )^{2}}
{36} -\frac{\left (x+4\right )^{2}}
{9} = 1
\]
\(20\)
\(16\)
\(10\)
\(8\)
2010005902
Level:
B
Find the distance between the points of intersection of the given hyperbola with the given straight line $q$.
\[
H\colon \frac{\left (y+6\right )^{2}}
{10} -\frac{\left (x-5\right )^{2}}
{6} = 1;\quad q\colon y+1 = 0
\]
\(6\)
\(8\)
\(10\)
\(12\)
2010005907
Level:
B
Find the vertex of the following parabola.
\[
y^{2} + 12x - 6y - 15 = 0
\]
\([2;3]\)
\([-2;3]\)
\([2;-3]\)
\([-2;-3]\)
2010005909
Level:
B
Which of the given points is one of the vertices of the hyperbola \(25y^{2} - 4x^{2} - 24x + 50y - 111 = 0\)?
\([-3;1]\)
\([3;1]\)
\([-3;4]\)
\([3;4]\)