Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ± 6)

Solution:

Length of major axis 26,

Foci (0, ±6)

Since the foci are on the y-axis, the major axis is along the y-axis

Therefore,

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

Accordingly,

2b = 16 ⇒ b = 8 and c = 6

It is known that a² = b² + c²

Hence,

⇒ a² = 8² + 6²

⇒ a² = 64 + 36

⇒ a² = 100

⇒ a = √100 = 10

Thus, the equation of the ellipse is x²/8² + y²/(10)² = 1 or x²/64 + y²/100 = 1

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 16

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ± 6).

Summary:

The equation of the ellipse is x²/64 + y²/100 = 1 while the Length of major axis 16, foci (0, ± 6)