This precalculus conic sections quiz asks 10 multiple-choice questions on conic sections: parabolas, ellipses and hyperbolas, and each answer comes with a short explanation.
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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How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
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.
How to use this precalculus conic sections quiz
Retake this precalculus conic sections quiz until every answer is right, then move on to the worksheet and the test.
