Given, e=21 and ea=4
⇒a=2,
Also, b2=a2(1−e2)
⇒b2=3
Equation of ellipse is 4x2+3y2=1
We know that, equation of normal to the ellipse a2x2+b2y2=1 at (x1,y1) is x1a2x−y1b2y=a2−b2
So, equation of normal at (1,23) is 14x−3/23y=4−3
⇒4x−2y=1
The eccentricity of an ellipse whose centre is at the origin is 21 . If one of its directrices is x=−4 , then the equation of the normal to it at (1,23) is:
Held on 2 Apr 2017 · Verified 6 Jul 2026.
2y−x=2
4x−2y=1
4x+2y=7
x+2y=4
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