Question

Find the equation of the ellipse whose foci are 0 + - 6 and the length of whose my axis 16

Answer 1

Correct Question :-

Find the equation of ellipse whose foci are (0, ±6) and length of whose minor axis is 16

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Here we have,

Foci of ellipse lie on the y axis (Given)

Hence,

It is a Vertical ellipse

Now,

Assume

${\boxed{\sf\:{Equation=\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1}}}$

Where a² > b²

Assume

c² = (a² - b²)

Foci = (0 , ±c)

Hence,

c = 6

$\tt{\rightarrow a=\dfrac{1}{2}\times 16}$

= 8

Now,

a² = (c² - b²)

= (36 + 64)

= 100

Hence,

a² = 100

b² = 64

Hence

$\Large{\boxed{\sf\:{Equation=\dfrac{x^2}{64}+\dfrac{y^2}{100}=1}}}$