The locus of the middle points of chords of the parabola y2=8x drawn through the vertex is a parabola whose

Question

The locus of the middle points of chords of the parabola y2=8x drawn through the vertex is a parabola whose (A) focus is (2, 0)  (B) latusrectum =8  (C) focus is (0, 2)  (D) latusrectum =4

Tardigrade Admin · Accepted Answer

If the middle point of a chord is (α , β ), then α =(2t2+0/2), β =(4t+0/2) On eliminating t , we get α =( (β /2) )2 ∴ Locus is x=(y2/4) ⇒ y2=4x This is the equation of parabola with latusrectum 4

Q. The locus of the middle points of chords of the parabola $y^{2} = 8 x$ drawn through the vertex is a parabola whose

focus is $(2, 0)$

latusrectum $= 8$

focus is $(0, 2)$

latusrectum $= 4$

If the middle point of a chord is $(α, β),$ then $α = \frac{2 t ^{2} + 0}{2}, β = \frac{4 t + 0}{2}$
On eliminating $t$ , we get $α = (\frac{β}{2})^{2}$
$∴$ Locus is $x = \frac{y ^{2}}{4}$
$\Rightarrow$ $y^{2} = 4 x$
This is the equation of parabola with latusrectum $4$

Q. The locus of the middle points of chords of the parabola y2=8x drawn through the vertex is a parabola whose

focus is (2,0)

latusrectum =8

focus is (0,2)

latusrectum =4