1) 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 A) $x^{2}=y$ B) $y^{2}=2x$ C) $y^{2}=x$ D) $x^{2}=2y$ Answer: Option CExplanation:By section formula $h=\frac{x+0}{4}, k=\frac{y+0}{4}$ $\therefore$ x-=4h, and y=4k Substituting in y2=4x $(4k)^{2}=4(4h) \Rightarrow k^{2}=h$ or $y^{2}=x$ is required locus
