A radius vector of point A relative to the origin varies with time t as `vec r = at hat i - bt^2 hat j` where `a and b` are constant. The equation of point's trajectory is.

Options

A. `y = -(b)/(a^2) x^2`
B. `y = (b)/(a^2) x^2`
C. `y = -(2 b)/(a^2) x^2`
D. `y = (2 b)/(a^2) x^2`

Answer

A

Explanation

`vec r = at hat i- bt^2 hat j`
`x = at and y = -bt^2`
`rArr t = ((x)/(a))and y = -b((x)/(a))^2 rArr y = (-b)/(a^2) x^2`.