Circles

Circle From Center and Radius

Write a circle equation from its center and radius using exact coordinates and radius squared.

circle-from-center-radius A circle with center (h, k) and radius r has equation (x-h)^2 + (y-k)^2 = r^2.

Example

Use a center and radius to write and plot a circle.

highlighted = computed this step

Step 1 — Plot the circle

Plot the center and radius.

Coordinate plot\text{Coordinate plot}
Circle from center-radius plotCircle centered at C(2, -3) with radius 5.C

Step 2 — Center

Read the center point.

C=(2,-3)C=( \hl{2} , \hl{-3} )

Step 3 — Radius

Square the radius.

r=5,r2=25r= 5 , r^{2}= \hl{25}

Step 4 — Equation

Write the circle in standard form.

(x−2)2+(y+3)2=25(x- \hl{2} )^{2} + (y+ \hl{3} )^{2} = \hl{25}