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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 an equation for the conic that satisfies the given conditions.

32. Parabola, focus (0, 0), directrix y = 6

To determine

To Find: The equation for the conic using the focus (0,0) and directrix y=6 of the parabola.

Explanation

Given:

Focus is (0,0) and directrix y=6 of the parabola.

Calculation:

Compute the distance from the focus to the directrix.

2p=focusofyaxisdirectrix

Substitute 0 for focus of y axis and 6 for directrix in above equation.

2p=062p=06p=62p=3

Compute the value of k using the below focus equation

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

The value of h=0

(k+p)=0 (1)

Substitute the value 3 for p in equation (1).

(k+(3))=0k=3

Then the directrix is located in the y axis

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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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