Find the equation for the ellipse that satisfies the given conditions: Foci (± 3, 0), a = 4

Solution:

Foci (± 3, 0), a = 4

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,

a = 4 and c = 3.

It is known that a² = b² + c²

Hence,

⇒ 4² = b² + 3²

⇒ 16 = b² + 9

⇒ b² = √16 - 9

⇒ b = √7

Thus, the equation of the ellipse is x²/4² + y²/(√7)² = 1 or x²/16 + y²/7 = 1

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 17

Find the equation for the ellipse that satisfies the given conditions: Foci (± 3, 0), a = 4

Summary:

The equation of the ellipse is x²/16 + y²/7 = 1 while Foci is (± 3, 0) and the value of a is 4