The equation of the normal to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` at the positive end of the latus rectum is

Options

A. `x+ey+e^(3)a=0`
B. `x-ey-e^(3)a=0`
C. `x " " ey-e^(2)a=0`
D. None of these

Explanation

The equation of the normal at `(x_(1),y_(1))` to the given ellipse is `(a^(2)x)/(x_(1))-(b^(2)y)/(y_(1))=a^(2)-b^(2)`.
Here, `x_(1)`= ae and `y_(1)=(b^(2))/(a)`
So the equation of the normal at the positive end of the latus rectum is
`(a^(2)x)/(ae)-((b^(2))/(y))/((b^(2))/(a))=a^(2)e^(2) " " [:'b^(2)=a^(2)(1-e^(2))]`
`rArr(ax)/(e)=a^(2)e^(2)rArrx-ey-e^(3)a=0`.