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

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

congruent segments

step-by-step explanation: