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Expert-verified Found in: Page 654 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Find the intercepts of the equation ${y}^{2}=16-4{x}^{2}$.

$\left(2,0\right),\left(-2,0\right),\left(0,-4\right)and\left(0,4\right)$ are the intercepts for equation ${y}^{2}=16-4{x}^{2}$.

See the step by step solution

## Step 1. Given information

Given Expression:

${y}^{2}=16-4{x}^{2}$

We want to find the intercepts of the given expression.

## Step 2. Finding the x-intercepts

The x-intercept is the point where the graph described with the given equation crosses the x-axis At the point $y=0$

Therefore, set $y=0$ and solve the quation for $x:$

${y}^{2}=16-4{x}^{2}\phantom{\rule{0ex}{0ex}}0=16-4{x}^{2}\phantom{\rule{0ex}{0ex}}4{x}^{2}=16\phantom{\rule{0ex}{0ex}}{x}^{2}=4\phantom{\rule{0ex}{0ex}}x=±2$

Therefore, there are two intercepts and they are $\left(2,0\right)and\left(-2,0\right)$

## Step 3. Finding the y-intercepts:

The y-intercept is the point where the graph described with the given equation crosses the y-axis At this point $x=0$.

Therefore, set $x=0$ and solve the equation for $y:$

${y}^{2}=16-4{x}^{2}\phantom{\rule{0ex}{0ex}}{y}^{2}=16-4{\left(0\right)}^{2}{y}^{2}=16\phantom{\rule{0ex}{0ex}}y=±4$

Therefore there are two y-intercepts and they are $\left(0,-4\right)and\left(0,4\right).$

## Step 4. Conclusion:

To conclude, there are a total of four intercepts for the given equation:

$\left(2,0\right),\left(-2,0\right),\left(0,-4\right)and\left(0,4\right)$ ### Want to see more solutions like these? 