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Chapter 10: Q. 46 (page 644)

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

x-22=4y-3

Short Answer

Expert verified

The vertex is 2,3,focus is 2,4and the directrix is y=2.

The graph of the equation x-22=4y-3shown below .

Step by step solution

01

Step 1. Given information .

Consider the given equationx-22=4y-3.

02

Step 2. Analyze the equation .

The standard form of parabola is x-h2=4y-3.

Compare the given equation with standard form.

x-h2=4ay-kx-22=4y-34a=4a=1h=2,k=3

Further simplify.

Since the value ofa=1then the vertex ish,k=2,3,focus ish,k+a=2,4and the directrix isy=k-a=2.

03

Step 3. Plot the graph .

By using the graphing utility the graph of the equation x-22=4y-3just shown below .

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

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