Skip to lesson

Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Precalculus · Chapter 2 · Lesson 1

Practice Worksheet

Circles and Ellipses

Slicing a cone, and what the equation records.

11 problems · about 24 minutes · TEKS P.3.B, P.3.E

NameDate

Figure — use these to answer the problems

Change the radius and watch the circumference and area follow.
d = 8
  • Diameter8 cm
  • Circumference25.13 cm
  • Area50.27 cm²
  • Circumference ÷ diameter3.14
Radius4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. (x − 5)² + (y + 1)² = 36. Radius?

    Answer

  2. (x − 2)² + (y − 5)² = 9. Radius?

    Answer

  3. Same circle. y of the centre?

    Answer

  4. (x + 4)² + y² = 16. x of the centre?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Match each equation form to the conic it describes.

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

    • Two squares added, equal coefficients
    • Two squares added, different coefficients
    • Two squares subtracted
    • Only one squared term
    • Circle
    • Ellipse
    • Hyperbola
    • Parabola

  2. x² + y² = 100. Radius?

    Answer

  3. How many conic sections come from slicing a double cone?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each equation by its conic.

    Write each item under the heading it belongs to: x² + y² = 4 · x² − y² = 4 · y = x² + 1

    Circle

    Hyperbola

    Parabola

  2. (x − 6)² + (y − 6)² = 1. Radius?

    Answer

  3. The Radius

    (x − 1)² + (y − 4)² = 49. What is the radius?

    Answer

  4. The Centre

    Same circle. What is the x of the centre?

    Answer