Question

Consider the parabola $x^2+4y=0$. Let (a,b) be any fixed point inside the parabola and let 'S' be the focus of the parabola. Then the minimum value of SQ+PQ as point Q moves on the parabola is

• A. |1-a|
• B. |ab|+1
• C. $\sqrt{a^2+b^2}$
• D. 1-b

Answer 1

The correct option is D 1-b

Let foot of perpendicular from Q to the directrix be N
$\Rightarrow$ SQ+PQ=QN+PQ is minimum if P,Q and N are collinear
So minimum value of SQ+PQ = PN = 1-b.