Question

Find an equation of the tangent line to the hyperbola

((x^2)/(a^2))-((y^2)/(b2))=1

at the point
(x0, y0).

Answer 1

(b^2)(x^2)-(a^2)(y^2)=(a^2)(b^2)
find y'
2b^2x-2a^2yy'=0
y'=(b^2x)/(a^2y)
y'=m
use point slope form (y-y0)=m(x-x0)