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प्रश्न
Find the equation for the ellipse that satisfies the given conditions:
Length of minor axis 16, foci (0, ±6)
उत्तर
Length of minor axis = 16; 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 `x^2/b^2 + y^2/a^2 = 1` where a is the semi-major axis.
Accordingly, 2b = 16 = b = 8 and c = 6
It is known that a2 = b2 + c2
∴ a2 = 82 + 62 = 64 + 36 = 100
= a = `sqrt100` = 10
Thus, the equation of the ellipse is `x^2/8^2 + y^2/10^2 = 1` or `x^2/64 + y^2/100 = 1`.
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