9000091209
Level:
A
Consider the circle \(k\colon x^{2} - 6x + y^{2} + 4y + 9 = 0\).
Find the center of the circle.
\(S = [3;-2]\)
\(S = [-3;-2]\)
\(S = [3;2]\)
\(S = [-3;2]\)
Conics
9000091210
Level:
A
Consider the circle \(k\colon x^{2} + 8x + y^{2} - 2y + 12 = 0\).
Find the center of the circle.
\(S = [-4;1]\)
\(S = [-4;-1]\)
\(S = [4;1]\)
\(S = [4;-1]\)
9000149701
Level:
A
Find the center of the following circle.
\[
x^{2} + y^{2} - 4x + 6y - 12 = 0
\]
\([2;-3]\)
\([-2;3]\)
\([2;3]\)
\([-2;-3]\)
9000149702
Level:
A
Find the center of the following circle.
\[
x^{2} + y^{2} + 2x - 8y + 13 = 0
\]
\([-1;4]\)
\([-1;-4]\)
\([1;4]\)
\([1;-4]\)
9000149703
Level:
A
Find the center of the following circle.
\[
x^{2} + y^{2} - 10x - 2y + 10 = 0
\]
\([5;1]\)
\([5;-1]\)
\([-5;1]\)
\([-5;-1]\)
9000149704
Level:
A
Find the center of the following ellipse.
\[
9x^{2} + 4y^{2} + 54x - 32y + 109 = 0
\]
\([-3;4]\)
\([-3;-4]\)
\([3;4]\)
\([3;-4]\)
9000149705
Level:
A
Find the center of the following ellipse.
\[
16x^{2} + 9y^{2} - 32x - 54y - 47 = 0
\]
\([1;3]\)
\([1;-3]\)
\([-1;3]\)
\([-1;-3]\)
9000168701
Level:
A
Which of the given points is one of the vertices on the major axis of the ellipse \(9x^{2} + 16y^{2} - 18x + 96y + 9 = 0\)?
\([5;-3]\)
\([4;-3]\)
\([1;1]\)
\([1;0]\)
9000168702
Level:
A
Given the ellipse \(4x^{2} + 9y^{2} + 16x - 18y - 11 = 0\),
find the coordinates of the vertex on the minor axis.
\([-2;3]\)
\([-2;4]\)
\([0;1]\)
\([1;1]\)
9000168703
Level:
A
Given the ellipse \(25x^{2} + 9y^{2} - 150x + 18y + 9 = 0\),
find the vertex on the major axis.
\([3;4]\)
\([3;2]\)
\([8;-1]\)
\([6;-1]\)