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Q. 38

Expert-verifiedFound in: Page 644

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

${y}^{2}=8x$

The vertex is $\left(0,0\right)$ focus is $\left(2,0\right)$ and directrix is $x=-2$ . The graph of the given equation is shown below .

Consider the given equation ${y}^{2}=8x$ .

The standard form of parabola is ${y}^{2}=4ax$ .

Compare the equation with standard form.

${y}^{2}=4ax\phantom{\rule{0ex}{0ex}}{y}^{2}=8x\phantom{\rule{0ex}{0ex}}4a=8\phantom{\rule{0ex}{0ex}}a=2$

Further simplify .

Since $a=2$ the vertex is $\left(0,0\right)$ ,the focus is $\left(a,0\right)=\left(2,0\right)$ and the directrix is $x=-a,x=-2$

The graph of the equation ${y}^{2}=8x$ using graphing utility is shown below .

Here V is the vertex , F is the focus and line $x=-2$ represents the directrix of the parabola .

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