Answer
$(x - 1)^2 + y^2 = 20$
Work Step by Step
First, we need to find the radius of the circle, so we need to see how far from the center the point given lies. Let us use the following distance formula to find the radius:
$r = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}$
We can now plug in our center, which is $(1, 0)$, and the coordinates of the point $(-3, 2)$ into this formula:
$r = \sqrt {(-3 - 1)^2 + (2 - 0)^2}$
Simplify what's in the parentheses:
$r = \sqrt {(-4)^2 + (2)^2}$
Evaluate the exponents:
$r = \sqrt {16 + 4}$
Simplify the radicand:
$r = \sqrt {20}$
Rewrite the radicand as the product of a perfect square and another factor:
$r = \sqrt {4 \cdot 5}$
Take the square root of the perfect square:
$r = 2\sqrt {5}$
Now, we can plug in the center and the radius into the standard equation for a circle, which is given by the formula:
$(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle, and $r$ is the radius.
Let us plug in our values:
$(x - 1)^2 + (y - 0)^2 = (2\sqrt {5})^2$
Evaluate what is in parentheses first:
$(x - 1)^2 + y^2 = (2\sqrt {5})^2$
Evaluate the exponent:
$(x - 1)^2 + y^2 = 2 \cdot 2 \cdot 5$
Multiply to simplify:
$(x - 1)^2 + y^2 = 20$
