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Chapter 10: Q. 50 (page 644)

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

y2-2y=8x-1

Short Answer

Expert verified

The vertex is -14,1,focus is 74,1and directrix is x=-94.

The graph of the equation shown below .

Step by step solution

01

Step 1. Given information .

Consider the given equationy2-2y=8x-1.y-k2=4ax-h

02

Step 2.  Analyze the equation .

The standard form of parabola is y-k2=4ax-h.

Compare the given equation with standard form .

role="math" localid="1647080511378" y-k2=4ax-hy-12=24x+1a=2h=-14,k=1

Further simplify .

Since the value ofa=2the vertex ish,k=-14,1,focus ish+a,k=74,1and directrix isx=h-a=-94.

03

Step 3. Plot the graph .

The graph of the parabola equation y-12=24x+1using graphing utility is shown below .

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