# 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 x^{2}/a^{2} + y^{2}/b^{2} = 1 where a is the semi major axis.

Accordingly,

2a = 26 ⇒ a = 13 and c = 5

It is known that a^{2} = b^{2} + c^{2}

Hence,

⇒ 13^{2} = b^{2} + 5^{2}

⇒ 169 = b^{2} + 25

⇒ b^{2} = 169 - 25

⇒ b^{2} = 144

⇒ b = 12

Thus, the equation of the ellipse is x^{2}/13^{2} + y^{2}/(12)^{2} = 1 or x^{2}/169 + y^{2}/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 x^{2}/169 + y^{2}/144 = 1 while the lengths of the major axis 26 and foci (± 5, 0)