Conic Sections: Parabolas, Ellipses and Hyperbolas: Precalculus Math Quiz – PDF Download
Ten quick multiple-choice questions on circles, parabolas, ellipses and hyperbolas: centers, foci, asymptotes, graphs and completing the square. Choose one answer for each, then read the explanation to see which common slip each wrong option represents.
🎯 Conic Sections: Parabolas, Ellipses and Hyperbolas – Precalculus math quiz
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Question 1
What is the center of the circle \((x-3)^{2}+(y+2)^{2}=16\)?
A\((3,\ -2)\)
B\((-3,\ 2)\)
C\((3,\ 2)\)
D\((-3,\ -2)\)
Question 2
What is the radius of the circle \(x^{2}+y^{2}-4x+2y-4=0\)?
A\(9\)
B\(3\)
C\(4\)
D\(6\)
Question 3
What is the focus of the parabola \(x^{2}=12y\)?
A\((0,\ 12)\)
B\((3,\ 0)\)
C\((0,\ 6)\)
D\((0,\ 3)\)
Question 4
The graph shows a parabola with focus \((2,\ 0)\) and directrix \(x=-2\). Which equation describes it?Focus and directrix of a parabola.
A\(x^{2}=8y\)
B\(y^{2}=8x\)
C\(y^{2}=4x\)
D\(y^{2}=-8x\)
Question 5
What are the foci of \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\)?
A\((\pm 5,\ 0)\)
B\((\pm 3,\ 0)\)
C\((\pm 4,\ 0)\)
D\((\pm\sqrt{34},\ 0)\)
Question 6
For the ellipse \(\frac{x^{2}}{36}+\frac{y^{2}}{20}=1\) shown, what is the sum of the distances from any point on the ellipse to the two foci?An ellipse with foci F.
A\(6\)
B\(8\)
C\(12\)
D\(16\)
Question 7
What are the asymptotes of \(\frac{x^{2}}{16}-\frac{y^{2}}{9}=1\)?
A\(y=\pm\frac{3}{4}x\)
B\(y=\pm\frac{4}{3}x\)
C\(y=\pm\frac{9}{16}x\)
D\(y=\pm\frac{16}{9}x\)
Question 8
A hyperbola has vertices \((\pm 3,\ 0)\) and foci \((\pm 5,\ 0)\), as shown. Which equation matches?Vertices orange, foci pink.
A\(\frac{x^{2}}{16}-\frac{y^{2}}{9}=1\)
B\(\frac{x^{2}}{9}+\frac{y^{2}}{16}=1\)
C\(\frac{y^{2}}{9}-\frac{x^{2}}{16}=1\)
D\(\frac{x^{2}}{9}-\frac{y^{2}}{16}=1\)
Question 9
Completing the square on \(4x^{2}+y^{2}-8x+6y+9=0\) shows which conic?
AAn ellipse
BA circle
CA parabola
DA hyperbola
Question 10
Which rule defines a hyperbola?
AThe sum of the distances to two fixed points is constant
BEach point is equally far from a fixed point and a fixed line
CThe absolute difference of the distances to two fixed points is constant
DEach point is the same distance from one fixed point
🎉 Quiz complete!
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Remember:
Circle: \((x-h)^{2}+(y-k)^{2}=r^{2}\), from the distance formula.
Parabola: \(x^{2}=4py\) has focus \((0,\ p)\) and directrix \(y=-p\).
Ellipse: \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) with \(c^{2}=a^{2}-b^{2}\); the distance sum is \(2a\).
Hyperbola: \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) with \(c^{2}=a^{2}+b^{2}\) and asymptotes \(y=\pm\frac{b}{a}x\).
Complete the square in \(x\) and \(y\) to rewrite a general conic equation in standard form.
