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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
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)
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