Q29. - Precalculus Enhanced with Graphing Utilities

Question

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

$\left(h,k\right)=\left(-1,-2\right)$ and $r=1$

Step-by-Step Solution

Answer

The standard form of the circle is .

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

Step 1. Given information.

Consider the given center and radius of the circle $\left(h,k\right)=\left(-1,-2\right)$and $r=1$.

Step 2. The standard form of the equation of circle is x - h 2 + y - k 2 = r 2 .

$$\begin{gathered} {\left(x+1\right)}^2+{\left(y+2\right)}^2=1^2 \\ {x}^2+1+2x+y^2+4+4y=1 \\ {x}^2+y^2+2x+4y+5=1 \\ {x}^2+y^2+2x+4y=-4 \end{gathered}$$