Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (± 5, 0)

Solution:

Lengths of major axis 26,

Foci (± 5, 0)

Since the foci are on the x-axis, the major axis is along the x-axis.

Therefore,

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

Accordingly,

2a = 26 ⇒ 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 x²/13² + y²/(12)² = 1 or x²/169 + y²/144 = 1

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 15

Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (± 5, 0)

Summary:

The equation of the ellipse is x²/169 + y²/144 = 1 while the lengths of the major axis 26 and foci (± 5, 0)