Find the x and y Intercepts (x-2)^2+(y+5)^2=9

${(x - 2)}^{2} + {(y + 5)}^{2} = 9$

Find the x-intercepts.

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

${(x - 2)}^{2} + {((0) + 5)}^{2} = 9$

Solve the equation.

Subtract ${((0) + 5)}^{2}$ from both sides of the equation.

${(x - 2)}^{2} = 9 - {((0) + 5)}^{2}$

Add $0$ and $5$ .

${(x - 2)}^{2} = 9 - 5^{2}$

Raise $5$ to the power of $2$ .

${(x - 2)}^{2} = 9 - 1 \cdot 25$

Multiply $- 1$ by $25$ .

${(x - 2)}^{2} = 9 - 25$

Subtract $25$ from $9$ .

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

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

$x - 2 = \pm \sqrt{- 16}$

Simplify $\pm \sqrt{- 16}$ .

Rewrite $- 16$ as $- 1 (16)$ .

$x - 2 = \pm \sqrt{- 1 (16)}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$x - 2 = \pm \sqrt{- 1} \cdot \sqrt{16}$

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

$x - 2 = \pm i \cdot \sqrt{16}$

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

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

Pull terms out from under the radical, assuming positive real numbers.

$x - 2 = \pm i \cdot 4$

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

$x - 2 = \pm 4 i$

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.

$x - 2 = 4 i$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$x = 4 i + 2$

Reorder $4 i$ and $2$ .

$x = 2 + 4 i$

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

$x - 2 = - 4 i$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$x = - 4 i + 2$

Reorder $- 4 i$ and $2$ .

$x = 2 - 4 i$

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

$x = 2 + 4 i, 2 - 4 i$

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

x-intercept(s): $None$

Find the y-intercepts.

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

${((0) - 2)}^{2} + {(y + 5)}^{2} = 9$

Solve the equation.

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

${(y + 5)}^{2} = 9 - {((0) - 2)}^{2}$

Subtract $2$ from $0$ .

${(y + 5)}^{2} = 9 - {(- 2)}^{2}$

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

${(y + 5)}^{2} = 9 - 1 \cdot 4$

Multiply $- 1$ by $4$ .

${(y + 5)}^{2} = 9 - 4$

Subtract $4$ from $9$ .

${(y + 5)}^{2} = 5$

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

$y + 5 = \pm \sqrt{5}$

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.

$y + 5 = \sqrt{5}$

Subtract $5$ from both sides of the equation.

$y = \sqrt{5} - 5$

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

$y + 5 = - \sqrt{5}$

Subtract $5$ from both sides of the equation.

$y = - \sqrt{5} - 5$

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

$y = \sqrt{5} - 5, - \sqrt{5} - 5$

y-intercept(s) in point form.

y-intercept(s): $(0, \sqrt{5} - 5), (0, - \sqrt{5} - 5)$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, \sqrt{5} - 5), (0, - \sqrt{5} - 5)$

Find the x and y Intercepts (x-2)^2+(y+5)^2=9

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