Q. The locus of the middle points of the chords of the parabola $y^{2} = 4ax,$ which passes through the origin is
A) $y^{2} = ax\$
B) $y^{2} = 2ax$
C) $y^{2} = 4ax$
D) $x^{2} = 4ay$
Explanation
(b)
Let mid point be $(h,\ k)$
$\therefore$ Equation of chord is
$T = S_{1}$
${yy}_{1} - 2a\left( x + x_{1} \right) = y_{1}^{2} - 4ax_{1}$
Since, it passes through origin
$\therefore\ - 2ax_{1} = y_{1}^{2} - 4ax_{1}$
$\Rightarrow \ \ y_{1}^{2} = 2ax_{1}$
$\therefore$ Locus is$\ y^{2} = 2ax$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.