Precalculus Examples

$y^{2} = 1296 - 36 x^{2}$

Step 1

Find the x-intercepts.

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Step 1.1

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

${(0)}^{2} = 1296 - 36 x^{2}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $1296 - 36 x^{2} = {(0)}^{2}$ .

$1296 - 36 x^{2} = {(0)}^{2}$

Step 1.2.2

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

$1296 - 36 x^{2} = 0$

Step 1.2.3

Subtract $1296$ from both sides of the equation.

$- 36 x^{2} = - 1296$

Step 1.2.4

Divide each term in $- 36 x^{2} = - 1296$ by $- 36$ and simplify.

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Step 1.2.4.1

Divide each term in $- 36 x^{2} = - 1296$ by $- 36$ .

$\frac{- 36 x^{2}}{- 36} = \frac{- 1296}{- 36}$

Step 1.2.4.2

Simplify the left side.

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Step 1.2.4.2.1

Cancel the common factor of $- 36$ .

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Step 1.2.4.2.1.1

Cancel the common factor.

$\frac{- 36 x^{2}}{- 36} = \frac{- 1296}{- 36}$

Step 1.2.4.2.1.2

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

$x^{2} = \frac{- 1296}{- 36}$

Step 1.2.4.3

Simplify the right side.

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Step 1.2.4.3.1

Divide $- 1296$ by $- 36$ .

$x^{2} = 36$

Step 1.2.5

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

$x = \pm \sqrt{36}$

Step 1.2.6

Simplify $\pm \sqrt{36}$ .

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Step 1.2.6.1

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

Step 1.2.6.2

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

$x = \pm 6$

Step 1.2.7

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

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Step 1.2.7.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 6$

Step 1.2.7.2

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

$x = - 6$

Step 1.2.7.3

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

$x = 6, - 6$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(6, 0), (- 6, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

$y^{2} = 1296 - 36 {(0)}^{2}$

Step 2.2

Solve the equation.

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Step 2.2.1

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

$y^{2} = 1296 - 36 \cdot 0$

Step 2.2.2

Multiply $- 36$ by $0$ .

$y^{2} = 1296 + 0$

Step 2.2.3

Add $1296$ and $0$ .

$y^{2} = 1296$

Step 2.2.4

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

$y = \pm \sqrt{1296}$

Step 2.2.5

Simplify $\pm \sqrt{1296}$ .

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Step 2.2.5.1

Rewrite $1296$ as $36^{2}$ .

$y = \pm \sqrt{36^{2}}$

Step 2.2.5.2

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

$y = \pm 36$

Step 2.2.6

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

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Step 2.2.6.1

First, use the positive value of the $\pm$ to find the first solution.

$y = 36$

Step 2.2.6.2

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

$y = - 36$

Step 2.2.6.3

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

$y = 36, - 36$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 36), (0, - 36)$

Step 3

List the intersections.

x-intercept(s): $(6, 0), (- 6, 0)$

y-intercept(s): $(0, 36), (0, - 36)$

Step 4