Let PQ be a double ordinate of the parabola, y2= - 4x, where P lies in the second quadrant. If R divides PQ in the ratio 2: 1, then the locus of R is :

Question

Let PQ be a double ordinate of the parabola, y2= - 4x, where P lies in the second quadrant. If R divides PQ in the ratio 2: 1, then the locus of R is : (A) 9y2 = 4x (B) 9y2 = - 4x (C) 3y2 = 2x (D) 3y2 = - 2x

Tardigrade Admin · Accepted Answer

Let P(-at21, 2at1), Q(-at21, -2at1) and R(h, k) By using section formula, we have h=-at21, k=(-2at1/3) k=-(2at1/3) ⇒ 3k=-2at1 ⇒ 9k2=4a2 t21=4a(-h) ⇒ 9k2=-4ah ⇒ 9k2=-4h ⇒ 9y2=-4x

Q. Let $PQ$ be a double ordinate of the parabola, $y^{2} = - 4 x$ , where P lies in the second quadrant. If R divides $PQ$ in the ratio $2 : 1$ , then the locus of R is :

$9 y^{2} = 4 x$

$9 y^{2} = - 4 x$

$3 y^{2} = 2 x$

$3 y^{2} = - 2 x$

Q. Let PQ be a double ordinate of the parabola, y2=−4x, where P lies in the second quadrant. If R divides PQ in the ratio 2:1, then the locus of R is :

9y2=4x

9y2=−4x

3y2=2x

3y2=−2x

LetP(−at12​,2at1​), Q(−at12​,−2at1​) and R(h,k) By using section formula, we have h=−at12​,k=3−2at1​​ k=−32at1​​ ⇒3k=−2at1​ ⇒9k2=4a2t12​=4a(−h) ⇒9k2=−4ah ⇒9k2=−4h ⇒9y2=−4x

Q. Let $PQ$ be a double ordinate of the parabola, $y^{2} = - 4 x$ , where P lies in the second quadrant. If R divides $PQ$ in the ratio $2 : 1$ , then the locus of R is :

$9 y^{2} = 4 x$

$9 y^{2} = - 4 x$

$3 y^{2} = 2 x$

$3 y^{2} = - 2 x$