1003020401
Level:
A
The equation of an ellipse is given by \( 5x^2+9y^2-30x-18y+9=0 \). The length of its semi-major axis is:
\( 3 \)
\( 5 \)
\( 9 \)
\( \sqrt5 \)
\( 14 \)
Conics
1003020402
Level:
A
The equation of an ellipse is given by \( x^2+4y^2-6x+32y+48=0 \). The length of its semi-minor axis is:
\( \frac52 \)
\( 5 \)
\( 25 \)
\( \frac{25}4 \)
\( \frac{15}2 \)
1003020403
Level:
A
An ellipse has the centre at \( S=[-1;3] \), the semi major axis with the length of \( 3 \) and the semi minor axis with the length of \( 2 \). The semi major axis is parallel to \( y \) axis. The equation of the ellipse is:
\( \frac{(x+1)^2}4+ \frac{(y-3)^2}9 = 1 \)
\( \frac{(x+1)^2}9 + \frac{(y-3)^2}4 = 1 \)
\( \frac{(x-1)^2}4+ \frac{(y+3)^2}9 = 1 \)
\( \frac{(x+1)^2}4-\frac{(y-3)^2}9 = 1 \)
\( \frac{(x+1)^2}4 + \frac{(y-3)^2}9 = -1 \)
1003024002
Level:
A
The equation of an ellipse is given by \( \frac{x^2}{48} +\frac{y^2}{36} = 1\). The point \( [-2;5] \) represents:
a point inside the ellipse
vertex of the ellipse
co-vertex of the ellipse
a point outside the ellipse
the centre of the ellipse
1103040101
Level:
A
The equation of an ellipse is given by \( \frac{(x-2)^2}4+y^2=1 \).
Which of the pictures below shows the given ellipse in the rectangular coordinate system?
1103040102
Level:
A
The diagram of an ellipse in the rectangular coordinate system is shown in the picture. Find the standard form equation of this ellipse:
\( \frac{(x-3)^2}4+\frac{(y-3)^2}9=1 \)
\( \frac{(x-3)^2}9+\frac{(y-3)^2}4=1 \)
\( \frac{(x+3)^2}4+\frac{(y+3)^2}9=1 \)
\( \frac{(x+3)^2}9+\frac{(y+3)^2}4=1 \)
1103040103
Level:
A
The diagram of an ellipse in the rectangular coordinate system is shown in the picture.What is the semi-major axis of this ellipse?
The segment \( SN \)
The segment \( SK \)
The line \( EF \)
The line \( KL \)
1103040106
Level:
A
A circle in the rectangular coordinate system is shown in the picture. What is the standard form equation of this circle?
\( x^2+(y-3)^2=4 \)
\( x^2+(y+3)^2=4 \)
\( x^2+(y-3)^2=2 \)
\( x^2+(y+3)^2=2 \)
1103040107
Level:
A
The picture below shows an ellipse drawn in the rectangular coordinate system. What is the semi-minor axis of this ellipse?
The segment \( SM \)
The segment \( SL \)
The line \( MN \)
The line \( EF \)
2010005908
Level:
A
Which of the given points is one of the co-vertices on the minor axis of the ellipse \(25x^{2} + 9y^{2} + 100x - 54y - 44 = 0\)?
\([-5;3]\)
\([-2;0]\)
\([-2;-2]\)
\([3;1]\)