Find the equations of the tangent and normal to the hyperbola `x^(2)/a^(2)-y^(2)/b^(2) = 1" at the point "(x_(0), y_(0))`.

Explanation

The equation of the given curve is `(x^2)/(a^2)−(y^2)/(b^2)=1` .....(i)


On differentiating both sides w.r.t `x`, we get


`(2x)/(a^2)−(2y)/(b^2)(dy/dx)=0⇒(dy)/(dx)=(b^2x)/(a^2y)`


∴ The slope of the tangent at `(x_0,y_0) =(dy/dx)_(x_0,y_0)=(b^2 x_0)/(a^2 y_0)`


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