Question

Assertion :The maximum value of $(\sqrt{-3+4x-x^2}+4{)}^2+(x-5{)}^2$ (where $1\le x\le 3)$ is $36$. Reason: The maximum distance between the point $(5,-4)$ and the point on the circle $(x-2{)}^2+y^2=1$ is $6$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Clearly by looking at equation it is distance between point $(5,-4)$
and circle $y=\sqrt{-3+4x-x^2}$ or $(x-2{)}^2+y^2=1$
Assume p is distance between centre of circle (2,0) and the point (5,-4)
$\Rightarrow p=\sqrt{(5-2{)}^2+(-4-0{)}^2}=5$
Hence maximum distance is $=5+1=6$
$\Rightarrow (\sqrt{-3+4x-x^2}+4{)}^2+(x-5{)}^2=36$
Thus the assertion is correct,
Reason is also explaining same thing, Therefore option 'A' is correct.