Find an equation of the tangent line to the curve at the given point. x2+2xy−y2+x=101, (7,9) (hyperbola)

The equation of the tangent line of the given curve

The tangent of the given curve at the point

Step-by-step explanation:

Explanation :-

Step(i):-

Given equation of the parabola

            x²+2xy−y²+x=101  ...(i)

apply derivative Formulas

   a)  

   b)  

Step(ii):-

Differentiating equation (i) with respective to 'x' , we get

on simplification , we get

The tangent of the given curve at the point ( 7,9)

Final answer :-

The equation of the tangent line of the given curve

The tangent of the given curve at the point