Find the x and y Intercepts (x-3)^2+(y+8)^2=16

${(x - 3)}^{2} + {(y + 8)}^{2} = 16$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

${(x - 3)}^{2} + {((0) + 8)}^{2} = 16$

Solve the equation.

Subtract ${((0) + 8)}^{2}$ from both sides of the equation.

${(x - 3)}^{2} = 16 - {((0) + 8)}^{2}$

Add $0$ and $8$ .

${(x - 3)}^{2} = 16 - 8^{2}$

Raise $8$ to the power of $2$ .

${(x - 3)}^{2} = 16 - 1 \cdot 64$

Multiply $- 1$ by $64$ .

${(x - 3)}^{2} = 16 - 64$

Subtract $64$ from $16$ .

${(x - 3)}^{2} = - 48$

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

$x - 3 = \pm \sqrt{- 48}$

Simplify $\pm \sqrt{- 48}$ .

Rewrite $- 48$ as $- 1 (48)$ .

$x - 3 = \pm \sqrt{- 1 (48)}$

Rewrite $\sqrt{- 1 (48)}$ as $\sqrt{- 1} \cdot \sqrt{48}$ .

$x - 3 = \pm \sqrt{- 1} \cdot \sqrt{48}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x - 3 = \pm i \cdot \sqrt{48}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$x - 3 = \pm i \cdot \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

$x - 3 = \pm i \cdot \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

$x - 3 = \pm i \cdot (4 \sqrt{3})$

Move $4$ to the left of $i$ .

$x - 3 = \pm 4 i \sqrt{3}$

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.

$x - 3 = 4 i \sqrt{3}$

Add $3$ to both sides of the equation.

$x = 4 i \sqrt{3} + 3$

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

$x - 3 = - 4 i \sqrt{3}$

Add $3$ to both sides of the equation.

$x = - 4 i \sqrt{3} + 3$

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

$x = 4 i \sqrt{3} + 3, - 4 i \sqrt{3} + 3$

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

${((0) - 3)}^{2} + {(y + 8)}^{2} = 16$

Solve the equation.

Subtract ${((0) - 3)}^{2}$ from both sides of the equation.

${(y + 8)}^{2} = 16 - {((0) - 3)}^{2}$

Subtract $3$ from $0$ .

${(y + 8)}^{2} = 16 - {(- 3)}^{2}$

Raise $- 3$ to the power of $2$ .

${(y + 8)}^{2} = 16 - 1 \cdot 9$

Multiply $- 1$ by $9$ .

${(y + 8)}^{2} = 16 - 9$

Subtract $9$ from $16$ .

${(y + 8)}^{2} = 7$

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

$y + 8 = \pm \sqrt{7}$

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.

$y + 8 = \sqrt{7}$

Subtract $8$ from both sides of the equation.

$y = \sqrt{7} - 8$

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

$y + 8 = - \sqrt{7}$

Subtract $8$ from both sides of the equation.

$y = - \sqrt{7} - 8$

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

$y = \sqrt{7} - 8, - \sqrt{7} - 8$

y-intercept(s) in point form.

y-intercept(s): $(0, \sqrt{7} - 8), (0, - \sqrt{7} - 8)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, \sqrt{7} - 8), (0, - \sqrt{7} - 8)$

Step 4

Find the x and y Intercepts (x-3)^2+(y+8)^2=16

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