9000168704
Level:
A
Given the ellipse \(9x^{2} + 4y^{2} + 36x - 24y + 36 = 0\),
find the vertex on the minor axis.
\([-4;3]\)
\([-5;3]\)
\([-2;0]\)
\([-2;1]\)
Conics
9000168705
Level:
A
Given the ellipse \(16x^{2} + 9y^{2} + 32x - 36y - 92 = 0\),
find the vertex on the major axis.
\([-1;-2]\)
\([-1;-1]\)
\([3;2]\)
\([2;2]\)
1003020404
Level:
B
The equation of a hyperbola is given by \( 9x^2-16y^2-108x+96y+36=0\). The length of its semi-major axis is:
\( 4 \)
\( 16 \)
\( 3 \)
\( 9 \)
\( 25 \)
1003020405
Level:
B
A hyperbola has two asymptotes with the equations \( y=\frac13(x+2) \) and \(y=-\frac13(x+2)\). What are the coordinates of its centre?
\( [-2;0] \)
\( [2;0] \)
\( \left[-\frac13;0\right] \)
\( [0;2] \)
\( \left[\frac13;2\right] \)
1003020406
Level:
B
The equation of a hyperbola is given by \( \frac{x^2}4-\frac{y^2}3=1 \). Which of the following are the asymptote equations of the hyperbola?
\( y=\pm\frac{\sqrt3}2x \)
\( x=\pm\frac{\sqrt3}2y \)
\( y=\pm\frac34 x \)
\( y=\pm\frac43 x \)
\( y=\pm\frac{2\sqrt3}3 x \)
1003020407
Level:
B
The equation of a hyperbola is given by \( \frac{(x-5)^2}{12}-\frac{(y+3)^2}8=1 \). The centre of the hyperbola has the coordinates:
\( [5;-3] \)
\( [-5;3] \)
\( [-5;-3] \)
\( [12;8] \)
\( [8;12] \)
1003020408
Level:
B
The equation of a hyperbola is given by \( \frac{x^2}9-\frac{y^2}{16}=1 \). What is the distance between its foci?
\( 10 \)
\( 5 \)
\( 16 \)
\( 9 \)
\( 4 \)
1003020409
Level:
B
The equation of a parabola is given by \( y^2 = 4x \). What is the parameter value of this parabola?
\( 2 \)
\( 4 \)
\( \frac12 \)
\( \frac14 \)
\( 1 \)
1003020410
Level:
B
The equation of a parabola is given by \( x^2+4y-6x+3=0 \). What is the parameter value of this parabola?
\( 2 \)
\( 4 \)
\( -2 \)
\( -4 \)
\( \frac32 \)
1003020411
Level:
B
A parabola has its focus \( F=[5;0] \) and the directrix with the equation \( x=0 \). What are the coordinates of its vertex?
\( \left[\frac52;0\right] \)
\( [0;0] \)
\( \left[0;\frac52\right] \)
\( [-5;0] \)
\( \left[-\frac52;0\right] \)