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Cogito

Precalculus · Chapter 2 · Lesson 2

Practice Worksheet

Parabolas and Hyperbolas

The other two conic sections.

12 problems · about 22 minutes · TEKS P.3.B, TEKS P.3.E

NameDate

Figure — use these to answer the problems

Move the vertex around. Every parabola has one focus, always inside the curve.
-8-8-6-6-4-4-2-222446688
y = 1x² + 0x + 0
a1
b0
c0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. y²/16 − x²/9 = 1. What is a, the value under the leading positive term?

    Answer

  2. What makes a parabola useful in a satellite dish?

    • Parallel rays all reflect through the focus.
    • It is a smooth round shape.

  3. x² + y² = 25. Conic type? 1 circle, 2 ellipse, 3 parabola, 4 hyperbola.

    Answer

  4. x²/9 − y²/4 = 1. Conic type? 1, 2, 3 or 4.

    Answer

  5. y = x². Conic type? 1, 2, 3 or 4.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. x²/16 + y²/9 = 1. Conic type? 1, 2, 3 or 4.

    Answer

  2. x²/4 − y²/9 = 1. What is a?

    Answer

  3. Same hyperbola. What is b?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Match each conic with what its equation looks like.

    Draw a line from each item on the left to its match on the right.

    • Parabola
    • Ellipse
    • Hyperbola
    • Only one variable squared
    • Two squares added
    • Two squares subtracted

  2. x²/36 − y²/36 = 1. What is the positive asymptote slope?

    Answer

  3. The Vertex

    (x − 4)² = 8(y − 2). What is the x-coordinate of the vertex?

    Answer

  4. The Slope

    x²/25 − y²/4 = 1. What is the positive asymptote slope, as a decimal?

    Answer