Find the x and y Intercepts x^2+y^2=25

$x^{2} + y^{2} = 25$

Step 1

Find the x-intercepts.

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

$x^{2} + {(0)}^{2} = 25$

Solve the equation.

Simplify $x^{2} + {(0)}^{2}$ .

Raising $0$ to any positive power yields $0$ .

$x^{2} + 0 = 25$

Add $x^{2}$ and $0$ .

$x^{2} = 25$

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

$x = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2}}$

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

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$

x-intercept(s) in point form.

x-intercept(s): $(5, 0), (- 5, 0)$

Step 2

Find the y-intercepts.

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

${(0)}^{2} + y^{2} = 25$

Solve the equation.

Simplify ${(0)}^{2} + y^{2}$ .

Raising $0$ to any positive power yields $0$ .

$0 + y^{2} = 25$

Add $0$ and $y^{2}$ .

$y^{2} = 25$

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

$y = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$y = \pm \sqrt{5^{2}}$

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

$y = \pm 5$

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.

$y = 5$

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

$y = - 5$

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

$y = 5, - 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5), (0, - 5)$

Step 3

List the intersections.

x-intercept(s): $(5, 0), (- 5, 0)$

y-intercept(s): $(0, 5), (0, - 5)$

Step 4

Find the x and y Intercepts x^2+y^2=25

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