Write as a Function of y (x-2)^2+y^2=64

${(x - 2)}^{2} + y^{2} = 64$

Step 1

Subtract $y^{2}$ from both sides of the equation.

${(x - 2)}^{2} = 64 - y^{2}$

Step 2

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x - 2 = \pm \sqrt{64 - y^{2}}$

Step 3

Simplify $\pm \sqrt{64 - y^{2}}$ .

Rewrite $64$ as $8^{2}$ .

$x - 2 = \pm \sqrt{8^{2} - y^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 8$ and $b = y$ .

$x - 2 = \pm \sqrt{(8 + y) (8 - y)}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x - 2 = \sqrt{(8 + y) (8 - y)}$

Add $2$ to both sides of the equation.

$x = \sqrt{(8 + y) (8 - y)} + 2$

Next, use the negative value of the $\pm$ to find the second solution.

$x - 2 = - \sqrt{(8 + y) (8 - y)}$

Add $2$ to both sides of the equation.

$x = - \sqrt{(8 + y) (8 - y)} + 2$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{(8 + y) (8 - y)} + 2$

$x = - \sqrt{(8 + y) (8 - y)} + 2$

$x = \sqrt{(8 + y) (8 - y)} + 2$

$x = - \sqrt{(8 + y) (8 - y)} + 2$

Step 5

To rewrite as a function of $y$ , write the equation so that $x$ is by itself on one side of the equal sign and an expression involving only $y$ is on the other side.

$f (y) = \sqrt{(8 + y) (8 - y)} + 2, - \sqrt{(8 + y) (8 - y)} + 2$

Write as a Function of y (x-2)^2+y^2=64

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