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Equation of a circle centred at the origin

Relate the constant to the squared radius.

  • A circle centred at the origin satisfies .
  • The right side is the squared radius, not the radius.

Example 1

Write the equation of a circle with centre (0, 0) and radius 2.

Use the squared radius on the right.Substitute the given radius.
Coordinate graph−4−3−2−11234−4−3−2−112340P

Example 2

Write the equation of a circle with centre (0, 0) and radius 3.

Use the squared radius on the right.Substitute the given radius.
Coordinate graph−4−224−4−2240P

Your turn

Question 1

Write the equation of a circle with centre (0, 0) and radius 4.

Check answer
Use the squared radius on the right.Substitute the given radius.
Coordinate graph−6−4−2246−6−4−22460P
Question 2

Write the equation of a circle with centre (0, 0) and radius 5.

Check answer
Use the squared radius on the right.Substitute the given radius.
Coordinate graph−6−4−2246−6−4−22460P
Question 3

Write the equation of a circle with centre (0, 0) and radius 6.

Check answer
Use the squared radius on the right.Substitute the given radius.
Coordinate graph−8−6−4−22468−8−6−4−224680P
Question 4

Write the equation of a circle with centre (0, 0) and radius 7.

Check answer
Use the squared radius on the right.Substitute the given radius.
Coordinate graph−8−6−4−22468−7.5−5−2.52.557.50P
Question 5

Write the equation of a circle with centre (0, 0) and radius 8.

Check answer
Use the squared radius on the right.Substitute the given radius.
Coordinate graph−10−7.5−5−2.52.557.510−10−7.5−5−2.52.557.5100P
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