Find the x and y Intercepts (x^2)/100+(y^2)/25=1

$\frac{x^{2}}{100} + \frac{y^{2}}{25} = 1$

Step 1

Find the x-intercepts.

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

$\frac{x^{2}}{100} + \frac{{(0)}^{2}}{25} = 1$

Solve the equation.

Simplify $\frac{x^{2}}{100} + \frac{{(0)}^{2}}{25}$ .

Simplify each term.

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

$\frac{x^{2}}{100} + \frac{0}{25} = 1$

Divide $0$ by $25$ .

$\frac{x^{2}}{100} + 0 = 1$

Add $\frac{x^{2}}{100}$ and $0$ .

$\frac{x^{2}}{100} = 1$

Multiply both sides of the equation by $100$ .

$100 \frac{x^{2}}{100} = 100 \cdot 1$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $100$ .

Cancel the common factor.

$100 \frac{x^{2}}{100} = 100 \cdot 1$

Rewrite the expression.

$x^{2} = 100 \cdot 1$

Simplify the right side.

Multiply $100$ by $1$ .

$x^{2} = 100$

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

$x = \pm \sqrt{100}$

Simplify $\pm \sqrt{100}$ .

Rewrite $100$ as $10^{2}$ .

$x = \pm \sqrt{10^{2}}$

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

$x = \pm 10$

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.

$x = 10$

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

$x = - 10$

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

$x = 10, - 10$

x-intercept(s) in point form.

x-intercept(s): $(10, 0), (- 10, 0)$

Step 2

Find the y-intercepts.

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

$\frac{{(0)}^{2}}{100} + \frac{y^{2}}{25} = 1$

Solve the equation.

Simplify $\frac{{(0)}^{2}}{100} + \frac{y^{2}}{25}$ .

Simplify each term.

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

$\frac{0}{100} + \frac{y^{2}}{25} = 1$

Divide $0$ by $100$ .

$0 + \frac{y^{2}}{25} = 1$

Add $0$ and $\frac{y^{2}}{25}$ .

$\frac{y^{2}}{25} = 1$

Multiply both sides of the equation by $25$ .

$25 \frac{y^{2}}{25} = 25 \cdot 1$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$25 \frac{y^{2}}{25} = 25 \cdot 1$

Rewrite the expression.

$y^{2} = 25 \cdot 1$

Simplify the right side.

Multiply $25$ by $1$ .

$y^{2} = 25$

Take the specified 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): $(10, 0), (- 10, 0)$

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

Step 4

Find the x and y Intercepts (x^2)/100+(y^2)/25=1

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