   Chapter 10.5, Problem 6E

Chapter
Section
Textbook Problem

Find the vertex, focus, and directrix of the parabola and sketch its graph.6. (y − 2)2 = 2x + 1

To determine

To Find: The vertex, focus, and directrix of the parabola for the equation (y2)2=2x+1.

Explanation

Given:

The parabola equation is as follows.

(y2)2=2x+1

Rewrite the equation.

(y2)2=2x+112(y2)2=12(x+12)

Calculation:

Compute the vertex of the parabola.

The equation of the vertex is given by

(yk)2=4p(xh)12(y2)2=12(x+12)

Then, the vertex is said to be (h,k).

Therefore, the vertex is (12,2).

Compute the focus of the parabola.

Compare the parabola equation with the below equation,

y2=4px

Take parabola equation as below.

12(y2)2=12(x+12)14p=121=2pp=12

The focus of the parabola can be said as below

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