Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ± 13), Foci (0, ± 5)

Solution:

Vertices (0, ± 13), Foci (0, ± 5)

Here, the vertices are on the x-axis.

Therefore,

the equation of the ellipse will be of the form x²/b² + y²/a² = 1 where a is the semi major axis.

Accordingly, a = 13 and c = 5

It is known that a² = b² + c²

Hence,

⇒ 13² = b² + 5²

⇒ 169 = b² + 25

⇒ b² = 169 - 25

⇒ b² = 144

⇒ b = 12

Thus, the equation of the ellipse is x²/12² + y²/13² = 1 or x²/144 + y²/169 = 1

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 11

Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ± 13), Foci (0, ± 5)

Summary:

The equation of the ellipse is x²/144 + y²/169 = 1 while Vertices is (0, ± 13) and Foci is (0, ± 5)