   Chapter 10.5, Problem 1E

Chapter
Section
Textbook Problem

# Find the vertex, focus, and directrix of the parabola and sketch its graph.1. x2 = 6y

To determine

To find: The vertex, focus and directrix of the parabola x2=6y.

Explanation

Given:

The parabola equation is x2=6y.

Calculation:

Compute the vertex of the parabola:

The equation of the vertex is as below.

(xh)2=4p(yk)x2=6y(x0)2=6(y0)

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

Therefore, the vertex is (0,0).

Compute the focus of the parabola.

Compare the parabola equation with the below equation.

x2=4py

Take the parabola equation as below.

4p=6p=64=32

Then, the focus of the parabola is said to be,

Focus=(h,k+p)=(0,(0+32))=(0,32)

Therefore, the focus of the parabola is (0,32)

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