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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

35-46 Finding the Equation of a Shifted Conic Find an equation for the conic section with the given properties.

The parabola with vertex V ( 3 , 5 ) and directrix y = 2

To determine

To find:

The equation of the parabola with vertex V(3,5) and directrix y=2.

Explanation

Given:

The vertex of the parabola is V(3,5).

The directrix of the parabola is y=2.

Approach:

For an equation in x and y, if the value of x is replaced by x±h, then the graph is shifted horizontally and if the value of y is replaced by y±k, then the graph is shifted vertically.

The equation of a parabola with vertex (h,k) and directrix y=a is given below.

(xh)2=4p(yk) … (1)

Calculations:

Consider the information provided about the hyperbola.

This implies that the parabola is facing upward.

The distance between the vertex and the directrix is given below.

p=52=3

The value 4p is given below

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Chapter 12 Solutions

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