QJEEM22Ma9654: JEE Main 2022 Mathematics - Class 11 JEEM22Ma9654 Solution: A particle is moving in the xy-plane along a curve C passing…

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