Let (x, y) be any point on the parabola y2=4 x. Let P be the point that divides the line segment from (0,0) to (x, y) in the ratio 1: 3. Then the locus of P is

Question

Let (x, y) be any point on the parabola y2=4 x. Let P be the point that divides the line segment from (0,0) to (x, y) in the ratio 1: 3. Then the locus of P is (A) x2=y (B) y2=2 x (C) y2=x (D) x2=2 y

Tardigrade Admin · Accepted Answer

y2=4 x and Q will lie on it ⇒ (4 k)2=4 × 4 h ⇒ k2=h ⇒ y2=x (replacing h by x and k by y)

Q. Let $(x, y)$ be any point on the parabola $y^{2} = 4 x$ . Let $P$ be the point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $1 : 3$ . Then the locus of $P$ is

$x^{2} = y$

$y^{2} = 2 x$

$y^{2} = x$

$x^{2} = 2 y$

$y^{2} = 4 x$
and $Q$ will lie on it
$\Rightarrow (4 k)^{2} = 4 \times 4 h$
$\Rightarrow k^{2} = h$
$\Rightarrow y^{2} = x$ (replacing h by x and k by y)

Q. Let (x,y) be any point on the parabola y2=4x. Let P be the point that divides the line segment from (0,0) to (x,y) in the ratio 1:3. Then the locus of P is

x2=y

y2=2x

y2=x

x2=2y