Equation of normal to hyperbola in different forms

Point form: Normal at (x1,y1)to hyperbola x²/a² - y²/b² = 1 is

x-x1/(x1/a²) = -(y-y1)/(y1/b²)

The equation can also be expressed as

a²x/x1 + b²y/y1 = a² + b²

Parametric form: Normal at (a sec θ , b tan θ)to hyperbola x²/a² - y²/b² = 1 is


a x cos θ + by cot θ = a² + b²