The set of values of 'a' for which the point (a-1, a+1) lies outside the circle `x^(2)+y^(2)=8` and inside the circle `x^(2)+y^(2)-12x+12y-62=0`, is

Options

A. `(-oo, -sqrt(3) ) uu(sqrt(3), oo)`
B. `(-3sqrt(2), 3 sqrt(2))`
C. `(-3sqrt(2), -sqrt(3))uu(sqrt(3), 3sqrt(2))`
D. none of these

Answer

C

Explanation

It is given that the point (a-1, a+1) lies outside the circle `x^(2)+y^(2)-12x+12y-62=0`. Therefore,
`(a-1)^(2)+(a+1)^(2)-8 gt 0`
and, `(a-1)^(2)+(a+1)^(2)-12(a-1)+12(a-1)+12(a+1)-62 lt 0`
`rArr 2a^(2)-6 gt 0 ` and `2a^(2)-36 lt 0`
`rArr a^(2)-3 gt 0 ` and `a^(2)-18 lt 0`
`rArr a in (-oo, -sqrt(3))uu(sqrt(3), oo)` and `a in (-3sqrt(2), 3sqrt(2))`
`rArr a in (-3sqrt(2), -sqrt(3))uu(sqrt(3),3sqrt(2))`