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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the vertex, focus, and directrix of the parabola and sketch its graph.

4. 3x2 + 8y = 0

To determine

To Find: The vertex, focus, and directrix of the parabola for the equation 3x2+8y=0.

Explanation

Given:

The parabola equation is as follows.

3x2+8y=0

Rewrite the equation as below.

x2=8y3

Calculation:

Compute the vertex of the parabola:

The equation of the vertex is as given.

(xh)2=4p(yk)x2=8y3(x0)2=83(y0)

Then, 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.

x2=8y34p=83p=83×14p=23

The focus of the parabola is to be computed as below.

Focus=(h,k+p)Focus=(0,(0+(23)))Focus=(0,23)

Therefore, the focus of the parabola is (0,23)

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