A particle moves along the curve `y=x^2+2xdot` At what point(s) on the curve are the `x` and `y` coordinates of the particle changing at the same rate?

Options

A. `1,3`
B. `(1/2,5/2)`
C. `(-1/2,-3/4)`
D. `(-1,-1)`

Answer

C

Explanation

According to condition `(dx)/(dt)=(dy)/(dt)`……………..i
Given equation of curve is
`y=x^(2)+2x`……………..ii
`implies(dy)/(dt)=(2x+2)(dx)/(dt)`
`implies(dy)/(dt)=(2x+2)(dx)/(dt)`
`implies1=2x+2` [ From Eq. i ]
`impliesx=-1//2`
Then from eq. ii `y=-3//4`
`:.` Point on the curve is `(-1/2,-3/4)`.