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Consider the parabola x^(2) +4y = 0. Let...

Consider the parabola `x^(2) +4y = 0`. Let `P(a,b)` be any fixed point inside the parabola and let S be the focus of the parabola. Then the minimum value at `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`

A

`|1 -a|`

B

`|ab|+1`

C

`sqrt(a^(2)+b^(2))`

D

`1-b`

Text Solution

Verified by Experts

The correct Answer is:
D

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