Find the equation of the ellipse in the following case: Length of minor axis 16 foci `(0,+-6)`

Explanation

Since the foci of the given ellipse lie on the y - axis, it is a vertical ellipse.
Let the required equation be `x^(2)/b^(2) + y^(2)/a^(2) = 1," where " a^(2) gt b^(2).`
Let ` c^(2) = (a^(2) - b^(2)).`
Then, its foci are `(0, pm c)` and therefore, c = 6.
Also, b = length of the semi-minor axis = `(1/2 xx 16) = 8.`
`:. a^(2) = (c^(2)+b^(2)) = (36 + 64) = 100.`
Thus, ` b^(2) = 64 and a^(2) = 100.`
Hence, the requation is `x^(2) /64 + y^(2)/100 = 1.`