# Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x-axis.

**Solution:**

It is given that

b = 3, c = 4, centre at the origin, foci on the x-axis.

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,

b = 3 and c = 4.

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

Hence,

⇒ a^{2} = 3^{2} + 4^{2}

⇒ a^{2} = 9 + 16

⇒ a^{2} = 25

⇒ a = √25

⇒ a = 5

Thus, the equation of the ellipse is x^{2}/5^{2} + y^{2}/3^{2} = 1 or x^{2}/25 + y^{2}/9 = 1

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 18

## Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x-axis.

**Summary:**

The equation of the ellipse is x^{2}/25 + y^{2}/9 = 1 while the foci are on the x-axis, the major axis is along the x-axis

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