9000105403
Level:
B
The parabola \(P\colon y^{2} + 2y + 10x - 24 = 0\) has
two \(y\)-intercepts.
Find their distance.
\(10\)
\(8\)
\(6\)
\(4\)
Conic Sections
9000105404
Level:
B
The parabola \(P\colon y^{2} + 4y + 6x - 5 = 0\) has
two \(y\)-intercepts.
Find their distance.
\(6\)
\(8\)
\(10\)
\(4\)
9000091208
Level:
A
Consider the circle \(k\colon x^{2} + 2x + y^{2} - 4y + 2 = 0\).
Find the center of the circle.
\(S = [-1,2]\)
\(S = [-1,-2]\)
\(S = [1,-2]\)
\(S = [1,2]\)
9000091209
Level:
A
Consider the circle \(k\colon x^{2} - 6x + y^{2} + 4y + 9 = 0\).
Find the center of the circle.
\(S = [3,-2]\)
\(S = [-3,-2]\)
\(S = [3,2]\)
\(S = [-3,2]\)
9000091210
Level:
A
Consider the circle \(k\colon x^{2} + 8x + y^{2} - 2y + 12 = 0\).
Find the center of the circle.
\(S = [-4,1]\)
\(S = [-4,-1]\)
\(S = [4,1]\)
\(S = [4,-1]\)
9000097002
Level:
B
Consider the parabola \((x - 4)^{2} = 8(y + 1)\).
Find the vertex of this parabola.
\([4,-1]\)
\([4,1]\)
\([1,4]\)
\([4,8]\)
9000097003
Level:
B
Consider the parabola \((x + 1)^{2} = 4(y - 3)\).
Find the focus of this parabola.
\([-1,4]\)
\([-1,3]\)
\([3,-1]\)
\([0,3]\)
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
\((x - 3)^{2} = 8y\).
\(y = -2\)
\(x = 3\)
\(x = 0\)
\(y = 0\)
9000097005
Level:
B
Consider the parabola \((x - 5)^{2} = -8(y - 3)\).
Find the vertex of this parabola.
\([5,3]\)
\([3,5]\)
\([5,-4]\)
\([-4,3]\)
9000097004
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
\((x + 2)^{2} = -8(y - 1)\).
\(y = 3\)
\(x = -2\)
\(x = 1\)
\(y = -4\)