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Two villages X & Y are on the same side of a straight river at distances ‘a’ & ‘b’ respectively from river. A pump set is to be installed by the river side at a point P. If the villages are situated a distance ‘c’, then

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Minimum value of $X P + P Y i s \sqrt{c^{2} + 2 a b}$

Minimum value of $X P + P Y i s \sqrt{c^{2} + 4 a b}$

Minimum value of $X P + P Y i s \sqrt{c^{2} - 4 a b}$

Minimum value of $X P + P Y i s \sqrt{c^{2} - 2 a b}$

answer is D.

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Detailed Solution

To find the point where pump set is to be installed reflect point ‘Y’ w.r.t. river say Y’ join with X intersection point of Y’X with river is the point ‘P’.

$X R = (a - b), Y R = \sqrt{c^{2} - {(a - b)}^{2}}$

$X Y' = \sqrt{c^{2} - {(a - b)}^{2} + {(a + b)}^{2}}$

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