   Chapter 10, Problem 20RE

Chapter
Section
Textbook Problem

# Finding the Standard Equation of an Ellipse In Exercises 17-20, find the standard form or the equation of the ellipse with the given characteristics.Foci: ( 0 , ± 7 ) Major axis length: 20

To determine

To calculate: The standard form of equation of an ellipse with Foci: (0,±7) and Major axis length 20.

Explanation

Given:

Foci: (0,±7)

Major axis length: 20

Formula used:

The standard equation of an ellipse with center (h,k), focus (h,k±c) and vertex (h,k±a) is (xh)2b2+(yk)2a2=1

Calculation:

The foci of the ellipse are given as (0,±7) and the major axis length as 20.

Observe the coordinates of the foci. It can be seen that the ellipse has a vertical major axis.

For an ellipse with vertical major axis, the center is (h,k), focus (h,k±c) and vertex (h,k±a).

Compare with the standard form,

h=0

Also,

Major axis length,

2a=20a=10

Here,

2k=7+(7)2k=0k=0

And,

k+c=7c=70=7

Now,

c2=a

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