JEE Advance - Mathematics (2011 - Paper 2 Offline - No. 6)
Let $$(x, y)$$ be any point on the parabola $${y^2} = 4x$$. 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
$${x^2} = y$$
$${y^2} = 2x$$
$${y^2} = x$$
$${x^2} = 2y$$
Explanation
Now, $${y^2} = 4x$$ and Q will lie on it.
$$ \Rightarrow {(4k)^2} = 4 \times 4h$$
$$ \Rightarrow {k^2} = h$$
$$ \Rightarrow {y^2} = x$$ (replacing h by x and k by y)
Comments (0)
