Question

The radius vector of a point A relative to the origin varies as $\overrightarrow{r}=at\hat{i}+b{t}^2\hat{j}$ where a and b are positive constants. Find the equation of trajectory.

• A. $y=\frac{b}{a^2}{x}^2$
• B. $y^2=\frac{b}{a^2}x$
• C. $y=\frac{a^2}{b}{x}^2$
• D. $\text{none of these}$

Answer 1

The correct option is A $y=\frac{b}{a^2}{x}^2$

Given $\overrightarrow{r}=at\hat{i}+b{t}^2\hat{j}=x\hat{i}+y\hat{j}$
$x=at,y=b{t}^2$

$\therefore y=b{\left(\frac{x}{a}\right)}^2$