   Chapter 12.4, Problem 40E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### 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 focus F ( 1 , 3 ) and directrix x = 3

To determine

To find:

The equation of the parabola with focus F(1,3) and directrix x=3.

Explanation

Given:

The foci of the parabola is F(1,3).

The directrix of the parabola is x=3.

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 x=a is given below.

(yk)2=4p(xh)… (1)

Calculations:

Consider the information provided about the hyperbola.

This implies that the parabola is facing towards left.

The vertex is the midpoint between the foci and the directrix.

The vertex of the parabola is given below.

V=(3+12,3+32)=(2,3)

The distance between the vertex and the directrix is given below

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