Question

Find equations of tangent and normal to the ellipse x2 a2 y2 b2 = 1

Answer 1

Answer:

x−ey−ae^3 =0

Step-by-step explanation:

The end of the latus rectum in the first quadrant is (ae, b^2/a)

Equation of normal at (ae, b^2/a) is

a^2x/ae - b^2y/b2/a = a^2 -

b^2 [ a^2x / x1 - b^2/y1 = a^2 - b^2 ]

⇒a/e x - ay = a^2e^2

[∵e^2 = a^2 −b^2/a^2 ]

⇒x−ey−ae^3 =0