Q28. - Precalculus Enhanced with Graphing Utilities

Question

Find the standard form of the equation of the circle whose center and radius are given.

$\left(h,k\right)=\left(-2,3\right)$ and $r=4$

Step-by-Step Solution

Answer

The standard form of the circle is .

$x^2+y^2+4x-6y=3$

Step 1. Given information.

Consider the given center and radius are$\left(h,k\right)=\left(-2,3\right)$ and $r=4$.

Step 2. Standard form of the circle is.

$$\begin{gathered} {\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2 \\ {\left(x+2\right)}^2+{\left(y-3\right)}^2=4^2 \\ {x}^2+y^2+4x-6y+13=16 \\ {x}^2+y^2+4x-6y=3 \end{gathered}$$