A point moves along the arc of parabola y=2 x^2 . Its abscissa increases uniformly at the rate of 2 units / sec . At the instant, the point is passing through (1,2) , its distance from origin is increasing at the rate of

Step-by-step solution

Given, d x dt =2 units/sec Given equation of parabola is y=2 x^2 Differentiating w.r.to t , we get aligned & d y dt =4 x d x dt & ~d y dt =8 x aligned (i) [ d x dt =2 ] The distance of point from origin is given by x^2+y^2 The rate of increasing distance of point from origin aligned & = d dt ( x^2+y^2 ) & = 1 2 x^2+y^2 ~d dt (x^2+y^2 ) & = 1 2 x^2+y^2 [2 x d x dt +2 y d y dt ] & = 1 2 x^2+y^2 [4 x+2 y 8 x] ...[From(i) & = (2 x+8 x y) x^2+y^2 aligned Since point is passing through (1,2) Rate of increasing distance o