The locus of a point which divides the line segment joining the point (0, -1) and a point on the parabola, x2 = 4y, internally in the ratio 1: 2, is :

Question

The locus of a point which divides the line segment joining the point (0, -1) and a point on the parabola, x2 = 4y, internally in the ratio 1: 2, is : (A) 9x2 - 12y = 8 (B) 4x2 - 3y = 2 (C) x2 - 3y = 2 (D) 9x2 -3y = 2

Tardigrade Admin · Accepted Answer

⇒ 3h = 2t and 3k = t2 - 2 ⇒ 3y=((3x/2))2-2 ⇒ 12y=9x2-8

Q. The locus of a point which divides the line segment joining the point (0, -1) and a point on the parabola, $x^{2} = 4 y$ , internally in the ratio 1 : 2, is :

$9 x^{2} - 12 y = 8$

$4 x^{2} - 3 y = 2$

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

$9 x^{2} - 3 y = 2$

$\Rightarrow 3 h = 2 t$ and $3 k = t^{2} - 2$
$\Rightarrow 3 y = (\frac{3 x}{2})^{2} - 2 \Rightarrow 12 y = 9 x^{2} - 8$

Q. The locus of a point which divides the line segment joining the point (0, -1) and a point on the parabola, x2=4y, internally in the ratio 1 : 2, is :

9x2−12y=8

4x2−3y=2

x2−3y=2

9x2−3y=2