Find the x and y Intercepts (x^2)/25-(y^2)/49=1

$\frac{x^{2}}{25} - \frac{y^{2}}{49} = 1$

Step 1

Find the x-intercepts.

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

$\frac{x^{2}}{25} - \frac{{(0)}^{2}}{49} = 1$

Solve the equation.

Simplify $\frac{x^{2}}{25} - \frac{{(0)}^{2}}{49}$ .

Simplify each term.

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

$\frac{x^{2}}{25} - \frac{0}{49} = 1$

Divide $0$ by $49$ .

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

Multiply $- 1$ by $0$ .

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

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

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

Multiply both sides of the equation by $25$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Multiply $25$ by $1$ .

$x^{2} = 25$

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 $y$ .

$\frac{{(0)}^{2}}{25} - \frac{y^{2}}{49} = 1$

Solve the equation.

Simplify $\frac{{(0)}^{2}}{25} - \frac{y^{2}}{49}$ .

Simplify each term.

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

$\frac{0}{25} - \frac{y^{2}}{49} = 1$

Divide $0$ by $25$ .

$0 - \frac{y^{2}}{49} = 1$

Subtract $\frac{y^{2}}{49}$ from $0$ .

$- \frac{y^{2}}{49} = 1$

Multiply both sides of the equation by $- 49$ .

$- 49 (- \frac{y^{2}}{49}) = - 49 \cdot 1$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 49 (- \frac{y^{2}}{49})$ .

Cancel the common factor of $49$ .

Move the leading negative in $- \frac{y^{2}}{49}$ into the numerator.

$- 49 \frac{- y^{2}}{49} = - 49 \cdot 1$

Factor $49$ out of $- 49$ .

$49 (- 1) \frac{- y^{2}}{49} = - 49 \cdot 1$

Cancel the common factor.

$49 \cdot - 1 \frac{- y^{2}}{49} = - 49 \cdot 1$

Rewrite the expression.

$- - y^{2} = - 49 \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y^{2} = - 49 \cdot 1$

Multiply $y^{2}$ by $1$ .

$y^{2} = - 49 \cdot 1$

Simplify the right side.

Multiply $- 49$ by $1$ .

$y^{2} = - 49$

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

$y = \pm \sqrt{- 49}$

Simplify $\pm \sqrt{- 49}$ .

Rewrite $- 49$ as $- 1 (49)$ .

$y = \pm \sqrt{- 1 (49)}$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$y = \pm \sqrt{- 1} \cdot \sqrt{49}$

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

$y = \pm i \cdot \sqrt{49}$

Rewrite $49$ as $7^{2}$ .

$y = \pm i \cdot \sqrt{7^{2}}$

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

$y = \pm i \cdot 7$

Move $7$ to the left of $i$ .

$y = \pm 7 i$

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.

$y = 7 i$

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

$y = - 7 i$

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

$y = 7 i, - 7 i$

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

y-intercept(s): $None$

Step 3

List the intersections.

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

y-intercept(s): $None$

Step 4

Find the x and y Intercepts (x^2)/25-(y^2)/49=1

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