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The greatest integral value of a such th...

The greatest integral value of `a` such that `sqrt( 9 - a^2 + 2x - x^2) >= sqrt(16 - x^2)` for at least one positive value of x is (a) 3 (b) 4 (c) 6 (d) 7

A

8

B

7

C

6

D

4

Text Solution

Verified by Experts

The correct Answer is:
2
`y= sqrt(9-a^(2)+2ax-x^(2))`
`y= sqrt(16-x^(2))`
`implies y^(2)+(x-a)^(2)=9`
`implies y^(2)+x^(2)=16`

If `agt 7` , no solution exist, So, `a le7`
Hence, maximum value of a is 7.
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