Question

find the equation of the ellipse in standard
if,
distance between its directrix is 10
which passes through (-√5, 2)​

Answer 1

The equation of the ellipse is x²/15 +y²/6 =1

1.given

2.distance between directrix is 10

3.2a/e=10

a=5e

x²/a²+y²/b²=1 is general equation of ellipse

satisfy(-√5,2) in above equation

4.5/a²+4/b²=1.........(1)

multiply b² to  1

5b²/a²+4=b²

we know b²=a²(1-e²)......(2)

b²/a²=(1-e²)

9 -5e²=b²

put b² and a² in (2)

9 -5e²=25e²(1-e²)

5e² -3=0

e²=3/5

substitute value of e² in above equations

so we get final equation to be

x²/15 +y²/6 =1