9000105401
Level:
B
The parabola \(P\colon x^{2} - 6x - 4y + 5 = 0\) has
two \(x\)-intercepts.
Find their distance.
\(4\)
\(6\)
\(8\)
\(10\)
Conics
9000105402
Level:
B
The parabola \(P\colon x^{2} - 4x - 10y - 21 = 0\) has
two \(x\)-intercepts.
Find their distance.
\(10\)
\(12\)
\(8\)
\(6\)
9000091201
Level:
A
Consider the circle \(k\colon x^{2} - 4x + y^{2} + 6y + 12 = 0\).
Find the radius of the circle.
\(1\)
\(2\)
\(3\)
\(4\)
9000091202
Level:
A
Consider the circle \(k\colon x^{2} + 6x + y^{2} + 2y + 6 = 0\).
Find the radius of the circle.
\(2\)
\(\sqrt{2}\)
\(3\)
\(4\)
9000091204
Level:
A
Consider the circle \(k\colon x^{2} + 4x + y^{2} - 8y + 11 = 0\).
Find the radius of the circle.
\(3\)
\(1\)
\(2\)
\(4\)
9000091205
Level:
A
Consider the circle \(k\colon x^{2} - 10x + y^{2} + 10y + 34 = 0\).
Find the radius of the circle.
\(4\)
\(2\)
\(3\)
\(1\)
9000091206
Level:
A
Consider the circle \(k\colon x^{2} - 4x + y^{2} + 6y + 11 = 0\).
Find the center of the circle.
\(S = [2;-3]\)
\(S = [2;3]\)
\(S = [-2;3]\)
\(S = [-2;-3]\)
9000091207
Level:
A
Consider the circle \(k\colon x^{2} - 6x + y^{2} + 2y + 6 = 0\).
Find the center of the circle.
\(S = [3;-1]\)
\(S = [-3;-1]\)
\(S = [3;1]\)
\(S = [-3;1]\)
9000097005
Level:
B
Consider the parabola \((x - 5)^{2} = -8(y - 3)\).
Find the vertex of this parabola.
\([5;3]\)
\([3;5]\)
\([5;-4]\)
\([-4;3]\)
9000091208
Level:
A
Consider the circle \(k\colon x^{2} + 2x + y^{2} - 4y + 2 = 0\).
Find the center of the circle.
\(S = [-1;2]\)
\(S = [-1;-2]\)
\(S = [1;-2]\)
\(S = [1;2]\)