Consider y = x2/a2 - y2/b2 = 1 as the equation of curve
By differentiating both sides w.r.t. x
By substituting the values
y – b tan θ = – (a tan θ/b sec θ) (x – a sec θ)
On further calculation
by sec θ – b2 tan θ sec θ = – ax tan θ + a2 sec θ tan θ
By taking sec θ tan θ as common
ax tan θ + by sec θ = sec θ tan θ(a2 + b2)
So we get
ax cos θ + by cot θ = a2 + b2