Question

Find an equation of the tangent line to the hyperbola: x^2/a^2 - y^2/b^2 = 1 at the point (x0,x1)

Answer 1

The standard form of a hyperbola is x2/a2 − y2/ b2 = 1
the tangent line is the first derivative of the functiony′ = b^2x/ a^2 y
hence the slope is m = b^2 x0 / a^2 x1

Therefore the equation of the tangent line isy−x1 = b^2 x0 / a^2 x1* (x−x0)