Consider y = x2/a2 + y2/b2 = 1 as the equation of curve
By differentiating both sides w.r.t. x
Here the equation of the normal at point (a cos θ, b sin θ)
On further calculation
yb cos θ – b2 sin θ cos θ = ax sin θ – a2 sin θ cos θ
It can be written as
a2 sin θ cos θ – b2 sin θ cos θ = ax sin θ – by cos θ
By taking sin θ cos θ as common
sin θ cos θ(a2 – b2) = ax sin θ – by cos θ
It can be written as
ax sec θ – by cosec θ = a2 – b2