# Find the equation

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)

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