   Chapter 12.4, Problem 37E ### 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 hyperbola with center C ( − 1 , 4 ) , vertices V 1 ( − 1 , − 3 ) and V 2 ( − 1 , 11 ) , and foci F 1 ( − 1 , − 5 ) and F 2 ( − 1 , 13 )

To determine

To find:

The equation of a hyperbola with center C(1,4), vertices V1(1,3) and V2(1,11), and foci F1(1,5) and F2(1,13).

Explanation

Given:

A hyperbola with center C(1,4), vertices V1(1,3) and V2(1,11), and foci F1(1,5) and F2(1,13).

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 hyperbola centred at (h,k) when the major axis is vertical is given by the following formula.

(yk)2a2(xh)2b2=1 … (1)

Calculations:

Consider the information provided about the hyperbola.

The center of the hyperbola is C(1,4).

The vertices of the hyperbola are V1(1,3) and V2(1,11).

The major axis is the vertical axis.

The length of the major axis is given below.

11(3)=14.

Therefore, the value of a is given below.

a=142=7

The coordinates of the foci are F1(1,5) and F2(1,13)

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