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Chapter 10: Q. 52 (page 644)

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

x2-4x=2y

Short Answer

Expert verified

The vertex is 2,-2, focus is 2,-32and the directrix is y=-52.

The graph of the equation shown below .

Step by step solution

01

Step 1. Given information .

Consider the given equationx2-4x=2y.

02

Step 2.  Analyze the equation .

The standard form of parabola is x-h2=4ay-k.

Compare the given equation with standard form .

x-h2=4ay-kx-22=2y+2a=12h=2,k=-2

x-h2=4ay-kx-22=2y+2a=12h=2,k=-2

Further simplify .

Since the value ofa=12the vertex ish,k=2,-2, focus ish,k+a=2,-32and the directrix isy=k-a=-52.

03

Step 3.  Plot the graph .

The graph of the equation x2-4x=2yusing graphing utility is shown below .

Here V is the vertex , F is focus and the liney=-52represents the directrix of the parabola .

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