Solve for y (x-2)^2+y^2=64

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

Subtract ${(x - 2)}^{2}$ from both sides of the equation.

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

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

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

Simplify $\pm \sqrt{64 - {(x - 2)}^{2}}$ .

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

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

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 $b = x - 2$ .

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

Simplify.

Subtract $2$ from $8$ .

$y = \pm \sqrt{(x + 6) (8 - (x - 2))}$

Apply the distributive property.

$y = \pm \sqrt{(x + 6) (8 - x - - 2)}$

Multiply $- 1$ by $- 2$ .

$y = \pm \sqrt{(x + 6) (8 - x + 2)}$

Add $8$ and $2$ .

$y = \pm \sqrt{(x + 6) (- x + 10)}$

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.

$y = \sqrt{(x + 6) (- x + 10)}$

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

$y = - \sqrt{(x + 6) (- x + 10)}$

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

$y = \sqrt{(x + 6) (- x + 10)}$

$y = - \sqrt{(x + 6) (- x + 10)}$

$y = \sqrt{(x + 6) (- x + 10)}$

$y = - \sqrt{(x + 6) (- x + 10)}$

Solve for y (x-2)^2+y^2=64

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