Equations of Circles

Apply prior geometry ideas in equations of circles.

Lesson 1 of 43 parts Practice Flashcards

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Center and Radius

Objective: Solve and explain center and radius.

A circle center (h,k), radius r has equation (x−h)²+(y−k)²=r².

Worked examples

Try itWrite the circle equation with center (1,3) and radius 3.Show answer

(x−1)²+(y−3)²=9. Substitute center and squared radius into standard form.

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Objective: Solve and explain center and radius.

A circle center (h,k), radius r has equation (x−h)²+(y−k)²=r².

Worked examples

Try itWrite the circle equation with center (1,3) and radius 3.Show answer

(x−1)²+(y−3)²=9. Substitute center and squared radius into standard form.

Objective: Solve and explain standard equation.

Identify center and radius from standard circle form.

Worked examples

Try itFor (x−1)²+(y+3)²=25, what is its center?Show answer

(1,−3). Read (h,k) from x−h and y−k.

Objective: Solve and explain testing points.

A point lies on a circle exactly when its coordinates satisfy the equation.

Worked examples

Try itIs (4,3) on circle (x−1)²+(y−3)²=9?Show answer

Yes. Substitution gives 3²+0²=9.

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