The parametric equations of curve $C$, is given as $x=at$, $y=a{{t}^{3}}$, where $a$ is a positive c

Question

The parametric equations of curve $C$, is given as $x=at$, $y=a{{t}^{3}}$, where $a$ is a positive constant. The point $P$ on the curve has parameter $p$ and the tangent to the curve at point $P$ cuts the $y$-axis at $S$ and the $x$-axis at $T$. The point $M$ is the midpoint of $ST$. Find a Cartesian equation of the curve traced by $M$ as $p$ varies. [5] Find the exact area bounded by curve $C$, the line $x=0$, $x=3$ and $x$-axis, giving your answer in terms of $a$. [3]

Accepted Answer

Midpoint locus $y=-\frac{27x^3}{a^2}$; area $=\frac{81}{4a^2}\text{ units}^2$

2018 EJC P1 Q3

2018 EJC P1 Q3

Video Solution: