11. Vertices (0, +13), foci (0, +5)

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Solution

The given vertices of ellipse are (0,±13) and foci are (0,±5) . (1)

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

Vertices of ellipse are represented as ( 0,±a ) when y is the major axis.(2)

Compare vertices in equation (1) and (2)

a=13

Foci of ellipse are represented as ( 0,±c ) when y is the major axis. (3)

Compare foci in equation (1) and (3).

c=5

Also, c 2 = a 2 − b 2 5 2 = 13 2 − b 2 b 2 =169−25 b =±12

Equation of ellipse is x 2 12 2 + y 2 13 2 =1

Therefore, the equation of ellipse with vertices ( 0,±13 ) and foci ( 0,±5 ) is x 2 144 + y 2 169 =1 .

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