Q 14. - Precalculus Enhanced with Graphing Utilities

Question

Write the standard form of the equation and the general form of the equation of each circle of radius $r$ and center $\left(h,k\right)$.

Graph each circle.

$r=3; (h,k)=(1,0)$

Step-by-Step Solution

Answer

Standard form of a circle is $(x-1{)}^2+(y-0{)}^2=3^2$

General form of a circle is $x^2+y^2-2x-8=0$

Graph is as follows:

Step 1. Given information

It is given that $r=3; (h,k)=(1,0)$

Step 2. Standard form of the circle

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

It is given that $r=3$ and $\left(h,k\right)=\left(1,0\right)$.

Therefore, the standard form of the circle is $(x-1{)}^2+(y-0{)}^2=3^2$

Step 3. General form of the circle

The general form of the circle is obtained by simplifying the standard form:

$\left(x^2-2x+1\right)+y^2=9$

Subtract $9$ from both sides

$x^2+y^2-2x-8=0$

Step 4. Graph of the circle

Graph is as follows: