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Question
Find the equation of the ellipse in the following case:
Length of minor axis 16 foci (0, ± 6)
Solution
\[\text{ Length of minor axis }=16 \text{ and foci }=\left( 0, \pm 6 \right)\]
\[\text{ i . e } . 2b = 16\]
\[ \Rightarrow b = 8\]
\[\text{ and } \]
\[\text{ be } = 6\]
\[ \Rightarrow e = \frac{6}{8}\]
We know that eccentricity e = `sqrt(("b"^2-"a"^2)/"b"^2)`
⇒ 6 = b`sqrt(("b"^2-64)/"b"^2)`
⇒ 36 = b2 - 64
⇒ b2 = 100
The equation of the ellipse is
⇒ `"x"^2/64+"y"^2/100 = 1`
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