# Chapter 2 - Section 2.4 - Circles - 2.4 Assess Your Understanding - Page 186: 16

Standard Form: $\color{blue}{(x-1)^2+y^2=9}$ General Form: $\color{magenta}{x^2+y^2-2x-3=0}$ Refer to the image below for the graph.

#### Work Step by Step

RECALL: The standard form of a circle's equation is: $(x-h)^2 +(y-k)^2=r^2$ where $r$ = radius and $(h, k)$ is the center. The circle has: center: $(h, k)=(1, 0)$ $r=3$ Substitute the given values of $h, k,$ and $r$ into the standard form above to obtain: $(x-1)^2+(y-0)^2=3^2 \\\color{blue}{(x-1)^2+y^2=9}$ Write the equation in general form by squaring each binomial then subtracting $4$ on both sides of the equation to obtain: $(x-1)^2+y^2=4 \\x^2-2x+1+y^2-4=0 \\\color{magenta}{x^2+y^2-2x-3=0}$ To graph the circle, perform the following steps: (1) Plot the center $(1, 0)$. (2) With a radius of $3$ units, plot the following points: 3 units to the left of the center: $(-2, 0)$ 3 units to the right of the center: $(4, 0)$ 3 units above the center: $(1, 3)$ 3 units below the center: $(1, -3)$ (3) Connect the four points above (not including the center) using a smooth curve to form a circle (Refer to the attached image in the answer part above for the graph.)

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.