Question

The locus of mid points of chords of the parabola $y^2=8x$ drawn through the vertex is a parabola whose

• A. focus is (2, 0)
• B. lotus rectum = 8
• C. focus is (0, 2)
• D. lotus rectum = 4

Answer 1

The correct option is D

lotus rectum = 4

The parabola is as given below,

AB is the chord with A fixed at the vertex of the parabola and

B moving along the parabola.

M(h,k) is the midpoint whose locus has to be found out.

If (x,y) is the point B on the parabola then,

$h=\frac{x}{2}$;$k=\frac{y}{2}$

$x=2h;y=2k$

since (x,y) lie on $y^2=8x$

$\Rightarrow (2k{)}^2=8.2h$

$4k^2=16h$

$k^2=4h$

$\therefore$ Equation of locus,

$y^2=4x$

lotus rectum=4

focus=(1,0)

correct option=(d)