Question

A curve has parametric equations x=2t-ln2t and y=t²-ln t² where t>0. Find the value of t at the point on the curve where dy/dx =2 . Hence ,find the coordinates of that point?

Answer 1

Coordinates of the point would be x=4-ln4 and y= 4-ln4

Explanation:

`dx/dt=2-1/t and dy/dt= 2t-2/t`

Since `dy/dx=2`, `2-1/t=t-1/t`. That gives t=2.

Hence coordinates of the point would be x=4-ln4 and y= 4-ln4