Question

Find the equation of the ellipse ,whose length of the major axis is 20 and foci ( 0+-5 )

Answer 1

$\huge\boxed{\underline{\mathfrak{Answer}}}$

[See the attachment please]

Answer 2

Correct Question :-

Find the equation of ellipse whose foci are (0, ±5) and length of whose major axis is 20

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

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 = 5

$\tt{\rightarrow a=\dfrac{1}{2}\times 20}$

= 10

Now,

c² = (a² - b²)

b² = (a² - c²)

= (100 - 25)

= 75

Hence,

a² = (10)²

= 100

b² = 75

Hence

$\Large{\boxed{\sf\:{Equation=\dfrac{x^2}{75}+\dfrac{y^2}{100}=1}}}$