   Chapter 10, Problem 45RE

Chapter
Section
Textbook Problem

# Find the foci and vertices and sketch the graph.45. x 2 9 + y 2 8 = 1

To determine

To find: The foci and vertices and sketch the graph of equation x29+y28=1 .

Explanation

Given:

The given equation is as follows.

x29+y28=1

(x0)2(3)2+(y0)2(22)2=1 (1)

Calculation:

The given equation is in the standard form of an ellipse equation.

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

Here, the variables h , k are the center of the ellipse, a is x-intercept, and b is y-intercept.

Compare equation (1) and (2).

So, the foci of an ellipse are located on the x axis using equation below.

x2a2+y2b2=1

h,k=(0,0)

Here in the given equation 9 is greater than 8 . So, 9 is taken as a2 .

a2=9 ; a=±3

b2=8 ; b=±22

Write the equation for c .

c=a2b2

Here, c is the distance of the foci from the center point

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