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Chapter 10: Q. 43 (page 644)

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

x-32=-y+1

Short Answer

Expert verified

The vertex is 3,-1,focus is 3,-54and directrix is -34.

The graph of the equation shown below.

Step by step solution

01

Step 1. Given information .

Consider the given equationx-32=-y+1

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-32=-y+14a=-1a=-14

h=3,k=-1

Further simplify .

Since the value ofa=-14then the vertex ish,k=3,-1and focus ish,k+a=3,-54and the directrix isy=k-a=-34

03

Step 3. Plot the graph .

The graph of the equation x-32=-y+1by using graphing utility just shown below.

Here V is the vertex , F is the focus and the line y=-34represents the directrix of the parabola .

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Most popular questions from this chapter

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

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