Statement 1: The maximum value of ${(\sqrt{- 3 + 4 x - x^{2}} + 4)}^{2} + {(x - 5)}^{2} (w h e r e 1 \leq x \leq 3) i s 36$
Statement 2: The maximum distance between the point $(5, - 4)$ and the point on the circle ${(x - 2)}^{2} + y^{2} = 1 i s 6$

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Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

Statement-1 is true, statement-2 is false.

Statement-1 is false, statement-2 is true.

answer is A.

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Detailed Solution

Let $y = \sqrt{- 3 + 4 x - x^{2}}$
$\Rightarrow x^{2} + y^{2} - 4 x + 3 = 0$
$∴$ point $(x, y)$ lies on this circle ${(x - 2)}^{2} + y^{2} = 1$
$C (2, 0)$ and radius 1
then the maximum distance between the point P and any point on the circles is 6
$\Rightarrow$ Maximum value of ${(\sqrt{- 3 + 4 x - x^{2}} + 4)}^{2} + {(x - 5)}^{2} i s 36$