Question

Find the equation of the ellipse in the following case:  

Length of minor axis 16 foci (0, ± 6)

Answer 1

\[\text{ Length of minor axis }=16 \text{ and foci }=\left( 0, \pm 6 \right)\]

\[\text{ i . e } . 2b = 16\]

\[ \Rightarrow b = 8\]

\[\text{ and } \]

\[\text{ be } = 6\]

\[ \Rightarrow e = \frac{6}{8}\]

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`