Question
The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is-
- 5x2 – 9y2 = 180
- 9x2 + 5y2 = 180
- x2 + 9y2 =180
- 5x2 + 9y2 = 180
Hint:
use the expressions for distances between focii and directrices to find the value of a,e,and b.
The correct answer is: x2 + 9y2 =180
5x2+9y2=100
2ae= 8 (distance between focii)
2a/e=18 (distance between directrix)
On multiplying both the equations, we get
4a2= 144
a2=36
a=6
e=8/12=2/3
b=a√1-e2
b2= 36(5/9)= 20
equation of ellipse:
x2/a2+y2/b2=1
x2/36+y2/20 = 1
5x2+9y2=100
the focii are located at (ae,0) and (-ae,0). the distance between them is (ae-(-ae))= 2ae
similarly, the directrices are at a/e and -a/e .
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