Answer :

Abscissa means the x-coordinate and ordinate means the y-coordinate


Slope of tangent is given as square of the difference of the abscissa and ordinate


Difference of abscissa and ordinate is (x – y) and its square will be (x – y)2


Hence slope of tangent is (x – y)2


Slope of tangent of a curve y = f(x) is given by



Substitute x – y = z hence y = x – z



Differentiate x – z with respect to x






Using partial fraction for




Equating numerator


A(1 – z) + B(1 + z) = 1


Put z = 1


B = 1/2


Put z = -1


A = 1/2


Hence



Put in (a)



Integrate



x = 1/2(log(1 + z) + (–log(1 – z)) + c


2x = log(1 + z) – log(1 – z) + c


Using log a – log b = log



Resubstitute z = x – y



Now it is given that the curve is passing through origin that is (0, 0)


Hence (0, 0) will satisfy the curve equation (b)


Putting values x = 0 and y = 0 in (b)



c = 0


Put c = 0 back in equation (b)





e2x(1 – x + y) = (1 + x – y)


Hence equation of curve is e2x(1 – x + y) = (1 + x – y)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Solve the followiRD Sharma - Volume 2

tan-1xMathematics - Exemplar

The number of solMathematics - Exemplar

Find the particulMathematics - Board Papers

Solve the followiRD Sharma - Volume 2

Find the particulMathematics - Board Papers