Q. 305.0( 1 Vote )

Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve any point (x, y) is

Answer :

Slope of tangent is given as


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




Integrate



Using partial fraction for




Equating numerator


A(x + 1) + Bx = 1


Put x = 0


A = 1


Put x = -1


B = -1


Hence


Hence equation (a) becomes




log(y – 1) = logx – log(x + 1) + c …(b)


Now it is given that the curve is passing through (1, 0)


Hence (1, 0) will satisfy the curve equation (b)


Putting values x = 1 and y = 0 in (b)


If we put y = 0 in (b) we get log (-1) which is not defined hence we must simplify further equation (b)


log (y – 1) – log x = – log (x + 1) + c


Using log a – log b = log




Using log a + log b = log ab



Take the constant c as log c so that we don’t have any undefined terms in our equation (Why only log c and not any other term because taking log c completely eliminates the log terms so we don’t have to worry about the undefined terms appearing in our equation)



Eliminating log



Now substitute x = 1 and y = 0



c = -2


Put back c = -2 in (c)



Hence the equation of curve is (y – 1)(x + 1) = -2x


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz on DIfferential CalculusInteractive Quiz on DIfferential CalculusInteractive Quiz on DIfferential Calculus50 mins
Interactive Quiz on Differential Calculus | Check YourselfInteractive Quiz on Differential Calculus | Check YourselfInteractive Quiz on Differential Calculus | Check Yourself56 mins
Functional Equations - JEE with easeFunctional Equations - JEE with easeFunctional Equations - JEE with ease48 mins
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