
Ellipse problem
Q)If the normal at the end of the latus rectum of an ellipse
x^2/a^2 + y^2/b^2=1
passes through one extemity of minor axis ,then the eccentricity of ellipse is given by ?
a)e^4+e^2+1=0
b)e^4+e^3+e^2+e +1=a
c)e^4+e^21=0
d)none of the above
Thanks in advance guys .

Hi sid 178, welcome to PF.
The coordinates of the one end of the latus rectum is ( ae, b^2/a).
The slope of the tangent at that point is given by
2x/a^2 + 2yy'/b^2 = 0
y' = [x1b^2/y1a^2]. Substitute the values of (x1, y1). You get
y' = .......?
Find the slope of the normal. The end point of the minor axis is ( 0, b).
m = [b^2/a + b]/ae.
Since tangent and normal are perpendicular to each other
m*y' = 1.
Simplify the result by using the relation b^2 = a^2( 1  e^2).
Answer: e^4 + e^2  1 = 0