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

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10

i think is g(1)=-1.

hope that i can