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Q. 3

Expert-verifiedFound in: Page 654

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Find the intercepts of the equation ${y}^{2}=16-4{x}^{2}$.

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

Given Expression:

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

We want to find the intercepts of the given expression.

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 $x:$

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

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

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 $y:$

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

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

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

$(2,0),(-2,0),(0,-4)and(0,4)$

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