A particle is moving in the xy-plane along a curve C passing through the point (3,3).

Question

A particle is moving in the $xy$-plane along a curve $C$ passing through the point $(3,3)$. The tangent to the curve $C$ at the point $P$ meets the $x$-axis at $Q$. If the $y$-axis bisects the segment $PQ$, then $C$ is a parabola with:

Accepted Answer

According to the question (Let P(x, y))

$$2x - y{{dx} \over {dy}} = 0$$

($$\because$$ equation of tangent at $$P:y - y = {{dy} \over {dx}}(y - x)$$)

$$\therefore$$ $$2{{dy} \over {y}} = {{dx} \over x}$$

$$ \Rightarrow 2\ln y = \ln x + \ln c$$

$$ \Rightarrow {y^2} = cx$$

$$\because$$ this curve passes through (3, 3)

$$\therefore$$ c = 3

$$\therefore$$ required parabola ${y^2} = 3x$ and L.R = 3

Solutions · 1