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 x²/a² + y²/b² = 1 where a is the semi-major axis.

Accordingly,

b = 3 and c = 4.

It is known that a² = b² + c²

Hence,

⇒ a² = 3² + 4²

⇒ a² = 9 + 16

⇒ a² = 25

⇒ a = √25

⇒ a = 5

Thus, the equation of the ellipse is x²/5² + y²/3² = 1 or x²/25 + y²/9 = 1

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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 x²/25 + y²/9 = 1 while the foci are on the x-axis, the major axis is along the x-axis