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Question

4centreattheorigin:focionthexaxis

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Solution

It is given that c=4 , b=3 ,center is at the origin and foci are on the x axis.

Since the foci are on the x axis, so the equation of the ellipse is represented as x 2 a 2 + y 2 b 2 =1 , where x is the major axis.(1)

The relationship between the semi-major and semi-minor axes and the distance of the focus from the center of the ellipse is represented as:

c= a 2 b 2

4= a 2 3 2 4 2 = a 2 3 2 a 2 =16+9 a=±5

Substitute the values of a and b in equation (1)

x 2 5 2 + y 2 3 2 =1 x 2 25 + y 2 9 =1

Therefore, the equation of the ellipse with c=4 , b=3 , center at origin and foci at x axis is x 2 25 + y 2 9 =1 .


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