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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Simplify $25 x^{2} + {(0)}^{2}$ .

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

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

Add $25 x^{2}$ and $0$ .

$25 x^{2} = 25$

Divide each term in $25 x^{2} = 25$ by $25$ and simplify.

Divide each term in $25 x^{2} = 25$ by $25$ .

$\frac{25 x^{2}}{25} = \frac{25}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 x^{2}}{25} = \frac{25}{25}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{25}{25}$

Simplify the right side.

Divide $25$ by $25$ .

$x^{2} = 1$

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

$x = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x = \pm 1$

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.

$x = 1$

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

$x = - 1$

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

$x = 1, - 1$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 1, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Simplify $25 {(0)}^{2} + y^{2}$ .

Simplify each term.

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

$25 \cdot 0 + y^{2} = 25$

Multiply $25$ by $0$ .

$0 + y^{2} = 25$

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): $(1, 0), (- 1, 0)$

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

Step 4

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

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