The locus of the mid point of the focal radii of a variable point P moving on the parabola y2=8 x, is a parabola whose latus rectum is

Question

The locus of the mid point of the focal radii of a variable point P moving on the parabola y2=8 x, is a parabola whose latus rectum is (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6b0394d87aec6037a4eef88de61aaf3e-.png" /> Clearly 2 h=a+a t2...(1) and 2 k =2 at ....(2) ∴ On eliminating t from(1) &(2), we get locus of M(h, k) is y2=4(x-1) ⇒ text Latus rectum =4

Q. The locus of the mid point of the focal radii of a variable point $P$ moving on the parabola $y^{2} = 8 x$ , is a parabola whose latus rectum is

1

2

3

4

Clearly $2 h = a + a t^{2}$ ...(1)
and $2 k = 2 a t$ ....(2)
$∴$ On eliminating $t$ from(1)\&(2),
we get locus of $M (h, k)$ is
$y^{2} = 4 (x - 1) \Rightarrow Latus rectum = 4$

Q. The locus of the mid point of the focal radii of a variable point P moving on the parabola y2=8x, is a parabola whose latus rectum is

1

2

3

4

Clearly 2h=a+at2...(1) and 2k=2at ....(2) ∴ On eliminating t from(1)\&(2), we get locus of M(h,k) is y2=4(x−1)⇒ Latus rectum =4

Q. The locus of the mid point of the focal radii of a variable point $P$ moving on the parabola $y^{2} = 8 x$ , is a parabola whose latus rectum is

Clearly $2 h = a + a t^{2}$ ...(1)
and $2 k = 2 a t$ ....(2)
$∴$ On eliminating $t$ from(1)\&(2),
we get locus of $M (h, k)$ is
$y^{2} = 4 (x - 1) \Rightarrow Latus rectum = 4$