The locus of the midpoints of all chords of the parabola y2 = 4ax through its vertex is another parabola with directrix

Question

The locus of the midpoints of all chords of the parabola y2 = 4ax through its vertex is another parabola with directrix (A) x = - a (B) x = a (C) x = 0 (D) x=-(a/2)

Tardigrade Admin · Accepted Answer

2h=at2, 2k=2at ⇒ t-k/a, ⇒ 2h =a (k2/a2), y2=2ax, Equation of its directr x=-a/2

Q. The locus of the midpoints of all chords of the parabola $y^{2} = 4 a x$ through its vertex is another parabola with directrix

$x = - a$

$x = a$

$x = 0$

$x = - \frac{a}{2}$

$2 h = a t^{2}, 2 k = 2 a t \Rightarrow t - k / a, \Rightarrow 2 h = a \frac{k ^{2}}{a ^{2}}, y^{2} = 2 a x$ , Equation of its directr $x = - a /2$

Q. The locus of the midpoints of all chords of the parabola y2=4ax through its vertex is another parabola with directrix

x=−a

x=a

x=0

x=−2a​