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Q. 3

Expert-verified
Found in: Page 582

Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

The standard equation of a circle with center at $\left(-2,5\right)$ and radius $3$ is ______ .

The standard equation of a circle with center at $\left(-2,5\right)$ and radius $3$ is ${\left(x+2\right)}^{2}+{\left(y-5\right)}^{2}=9.$

See the step by step solution

Step 1. Given Information

The given center of a circle is $\left(-2,5\right)$ and radius is $3.$

Step 2. Filling the blank

The standard equation of a circle with center $\left(h,k\right),$ and radius $r$ is ${\left(x-h\right)}^{2}+{\left(y-k\right)}^{2}={r}^{2}.$

So, the standard equation of a circle with center at $\left(-2,5\right)$ and radius $3$ is role="math" localid="1646719972363" ${\left(x+2\right)}^{2}+{\left(y-5\right)}^{2}={3}^{2}\phantom{\rule{0ex}{0ex}}{\left(x+2\right)}^{2}+{\left(y-5\right)}^{2}=9$