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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

SKILLS

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

The ellipse with vertices V 1 ( 1 , 4 ) and V 2 ( 1 , 6 ) , and foci F 1 ( 1 , 3 ) and F 2 ( 1 , 5 )

To determine

To find:

The equation of the ellipse with vertices V1(1,4) and V2(1,6), and foci F1(1,3) and F2(1,5).

Explanation

Given:

An ellipse with vertices V1(1,4) and V2(1,6), and foci F1(1,3) and F2(1,5).

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 an ellipse centred at (h,k) is given by the following formula.

(xh)2a2+(yk)2b2=1(1)

Calculations:

Consider the information provided about the ellipse.

The vertices of the ellipse are V1(1,4) and V2(1,6).

The major axis is the vertical axis.

The length of the major axis is given below.

6(4)=10

Therefore, the value a is given below.

a=102=5

The coordinates of the foci are F1(1,3) and F2(1,5).

Therefore, the value c is given below.

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