Find the x and y Intercepts x^2+49y^2=49

$x^{2} + 49 y^{2} = 49$

Step 1

Find the x-intercepts.

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

$x^{2} + 49 {(0)}^{2} = 49$

Solve the equation.

Simplify $x^{2} + 49 {(0)}^{2}$ .

Simplify each term.

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

$x^{2} + 49 \cdot 0 = 49$

Multiply $49$ by $0$ .

$x^{2} + 0 = 49$

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

$x^{2} = 49$

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

$x = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

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

$x = \pm \sqrt{7^{2}}$

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

$x = \pm 7$

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.

$x = 7$

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

$x = - 7$

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

$x = 7, - 7$

x-intercept(s) in point form.

x-intercept(s): $(7, 0), (- 7, 0)$

Step 2

Find the y-intercepts.

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

${(0)}^{2} + 49 y^{2} = 49$

Solve the equation.

Simplify ${(0)}^{2} + 49 y^{2}$ .

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

$0 + 49 y^{2} = 49$

Add $0$ and $49 y^{2}$ .

$49 y^{2} = 49$

Divide each term in $49 y^{2} = 49$ by $49$ and simplify.

Divide each term in $49 y^{2} = 49$ by $49$ .

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

Simplify the left side.

Cancel the common factor of $49$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $49$ by $49$ .

$y^{2} = 1$

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

$y = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$y = \pm 1$

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.

$y = 1$

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

$y = - 1$

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

$y = 1, - 1$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(7, 0), (- 7, 0)$

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

Step 4

Find the x and y Intercepts x^2+49y^2=49

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