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Chapter 10: Q. 38 (page 644)

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

y2=8x

Short Answer

Expert verified

The vertex is 0,0focus is 2,0and directrix is x=-2. The graph of the given equation is shown below .

Step by step solution

01

Step 1. Given information .

Consider the given equationy2=8x.

02

Step 2. Analyze the equation .

The standard form of parabola is y2=4ax.

Compare the equation with standard form.

y2=4axy2=8x4a=8a=2

Further simplify .

Since a=2the vertex is 0,0,the focus is a,0=2,0and the directrix isx=-a,x=-2

03

Step[ 3. Plot the graph .

The graph of the equation y2=8xusing graphing utility is shown below .

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

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