Question

What are the directrices of the ellipse given by the equation x^2/25 + y^2/9 =1?

Answer 1

a^2 = 25
b^2 = 9
For ellipse
a^2 = b^2 + c^2
c^2 = 25 - 9 = 16
c = 4
The eccentricity e is c/a
e = 4/5
The directrix is 1/e away from edge of ellipse
1/e = 5/4
center is (0,0)
edges of major axis at (-5,0) and (5,0)
directrices at x = +- 25/4