2010006008
Level:
B
Parabola is a set of points that are equidistant from the point (focus)
and the line (directrix). Find the equation of the directrix of the parabola
\(x^{2} + 4x +8y-20= 0\).
\(y-5 = 0\)
\(y-1 = 0\)
\(x = 0\)
\(x+4 = 0\)
Conics
2010006009
Level:
B
Find the distance between the point \([5;5]\)
and the focus of the parabola \(y^{2} +12x + 6y -15 = 0\).
\(10\)
\(8\)
\(3\sqrt{10}\)
\(2\sqrt{41}\)
2010006302
Level:
B
The equation of a hyperbola is given by \( -16x^2+9y^2-96x+108y+36=0\). The length of its semi-minor axis is:
\( 3 \)
\( 9\)
\( 4 \)
\( 16 \)
\( 5 \)
2010006303
Level:
B
A parabola passes through the points \( A=[5;0] \) and \( B=[-6;2] \) and it is symmetric with respect to \( x\)-axis. What are the coordinates of its vertex?
\( [5;0] \)
\( [6;-2] \)
\( [0;5] \)
\( [-6;2] \)
\( [-1;1] \)
2010006304
Level:
B
The equation of a parabola is given by \( y^2-x-6y+10=0 \). What are the coordinates of its vertex?
\( [1;3] \)
\( [3;1] \)
\( [3;-1] \)
\( [-1;-3] \)
\( [-3;-1] \)
2010006305
Level:
B
Decide whether the equation \( 9x^2+4y^2-18x+8y+14=0 \) (in \( x \)-\( y \) plane) describes:
an empty set
an ellipse
a parabola
a hyperbola
a point
2010006306
Level:
B
The equation of a hyperbola with the center \( S=[1;-3] \), the focus \( F=[1;2] \), and the vertex \( A=[1;0] \) is given by:
\( \frac{(y+3)^2}{9}-\frac{(x-1)^2}{16} =1 \)
\( \frac{(x-1)^2}{16}-\frac{(y+3)^2}{9} =1 \)
\( \frac{(x-1)^2}{9}-\frac{(y+3)^2}{16} =1 \)
\( \frac{(y+3)^2}{16}-\frac{(x-1)^2}{9} =1 \)
\( \frac{(x+1)^2}{16}-\frac{(y-3)^2}{9} =1 \)
2010006307
Level:
B
The equation of a parabola is given by \( 4x^2+16x-y+18=0 \). Find the equation of its directrix.
\( x=\frac{31}{16} \)
\( x=-\frac{33}{16} \)
\( x=\frac{33}{16} \)
\( x=-\frac{31}{16} \)
\( x=\frac{15}{8} \)
9000097001
Level:
B
Parabola is a set of the points that are equidistant from the point
(focus) and the line (directrix). Find the directrix of the parabola
\((x - 3)^{2} = 8y\).
\(y = -2\)
\(x = 3\)
\(x = 0\)
\(y = 0\)
9000097002
Level:
B
Consider the parabola \((x - 4)^{2} = 8(y + 1)\).
Find the vertex of this parabola.
\([4;-1]\)
\([4;1]\)
\([1;4]\)
\([4;8]\)