The locus of the centroid of triangle PSQ, where PQ is any chord of the parabola y2=8(.x+2.) subtending right angle at the vertex and S be its focus is also a parabola whose latus rectum is equal to

Question

The locus of the centroid of triangle PSQ, where PQ is any chord of the parabola y2=8(.x+2.) subtending right angle at the vertex and S be its focus is also a parabola whose latus rectum is equal to (A) (1/3) (B) (4/3) (C) (8/3) (D) 2

Tardigrade Admin · Accepted Answer

t1t2=-4 If (h , k) is the centroid of Δ PSQ, Then (3 h + 4/2)=t12+t22,(3 k/4)=t1+t2 ⇒ k2=(8/3)(.h-4.) ∴ Latus rectum =(8/3)

Q. The locus of the centroid of triangle $PSQ,$ where $PQ$ is any chord of the parabola $y^{2} = 8 (x + 2)$ subtending right angle at the vertex and $S$ be its focus is also a parabola whose latus rectum is equal to

$\frac{1}{3}$

$\frac{4}{3}$

$\frac{8}{3}$

$2$

$t_{1} t_{2} = - 4$
If $(h, k)$ is the centroid of $Δ PSQ,$
Then $\frac{3 h + 4}{2} = t_{1}^{2} + t_{2}^{2}, \frac{3 k}{4} = t_{1} + t_{2}$
$\Rightarrow k^{2} = \frac{8}{3} (h - 4)$
$∴$ Latus rectum $= \frac{8}{3}$

Q. The locus of the centroid of triangle PSQ, where PQ is any chord of the parabola y2=8(x+2) subtending right angle at the vertex and S be its focus is also a parabola whose latus rectum is equal to

31​

34​

38​

2

t1​t2​=−4 If (h,k) is the centroid of ΔPSQ, Then 23h+4​=t12​+t22​,43k​=t1​+t2​ ⇒k2=38​(h−4) ∴ Latus rectum =38​

Q. The locus of the centroid of triangle $PSQ,$ where $PQ$ is any chord of the parabola $y^{2} = 8 (x + 2)$ subtending right angle at the vertex and $S$ be its focus is also a parabola whose latus rectum is equal to

$\frac{1}{3}$

$\frac{4}{3}$

$\frac{8}{3}$

$2$

$t_{1} t_{2} = - 4$
If $(h, k)$ is the centroid of $Δ PSQ,$
Then $\frac{3 h + 4}{2} = t_{1}^{2} + t_{2}^{2}, \frac{3 k}{4} = t_{1} + t_{2}$
$\Rightarrow k^{2} = \frac{8}{3} (h - 4)$
$∴$ Latus rectum $= \frac{8}{3}$