Explanation
Let the arbitrary point be x,y. Now the slope of the line joining the origin and the point is =\dfrac{y-0}{x-0} =\dfrac{y}{x}. The equation of the curve y=f(x). Now slope of the tangent =\dfrac{dy}{dx} =\dfrac{y}{2x} ... as per the given condition. Hence 2\dfrac{dy}{y}=\dfrac{dx}{x} Integrating both sides we get 2\ln y=\ln x+\ln c Now y_{x=1}=2 Hence 2\ln (2)=\ln (1)+\ln (c) Or c=2^{2}=4 Hence 2\ln y=\ln x+\ln 4 Or \ln (y^{2})=\ln 4x Or y^{2}=4x is the required equation. This is an equation of parabola.
Please disable the adBlock and continue. Thank you.