Chapter 13, Problem 1RVS

To determine

The correct match of equation ${\left(x-1\right)}^2+{\left(y+3\right)}^2=9$ with its graph from the provided options.

Answer to Problem 1RVS

Solution:

The correct match of equation ${\left(x-1\right)}^2+{\left(y+3\right)}^2=9$ with its graph is C.

Explanation of Solution

Given information:

The given equation is, ${\left(x-1\right)}^2+{\left(y+3\right)}^2=9$

The provided options,

Consider the equation,

${\left(x-1\right)}^2+{\left(y+3\right)}^2=9$

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

Therefore,

${\left(x-1\right)}^2+{\left(y+3\right)}^2=9$

The given equation ${\left(x-1\right)}^2+{\left(y+3\right)}^2=9$ represents the graph of a circle with center $\left(1,-3\right)$ and radius 3.

Thus, the graph in option C matches to the equation ${\left(x-1\right)}^2+{\left(y+3\right)}^2=9$ that is shown below,