Equation of tangent

Equation of tangent

Let S ≡ −1 = 0 be a hyperbola. Then equation of the tangent to the hyperbola S = 0.

(a) at the point P(x1, y1) is T ≡   − 1 = 0

(b) at the point (a secθ, b tanθ) is   = 1

(c) in slope form is y = mx ± and the point of contact is

(d) The line y = mx + c is tangent to the hyperbola   = 1 if c² = a²m² − b²

Equation of normal

(a) Equation of normal to the hyperbola = 1 at the point (x1, y1) is y − y1 = − (x −x1)

(b) Equation of normal at (asecθ, btanθ) is axcosθ + bycotθ = a² + b²