1.

If `x+y=3` is tangent at `(2,1)` on hyperbola, intersects asymptotes at `A` and `B` such that `AB=8sqrt(2)`. If centre of hyperbola is `(-1,-1)`, then least possible value of sum of semi -transverset axis and semi -conjugate axis is `psqrt(q)` where HCF `(p,q)=1` and `sqrt(q)` is irrational number. then, `(p+q)` is equal to

Answer» Correct Answer - 9
`(x-2)/(-1/(sqrt(2)))=(y-1)/(1/(sqrt(2)))=4sqrt(2)` or `-4sqrt(2)`
`:. A(-2,5)` & `B(6, -3)`
`:.` area of `/_CAB=20`
`implies` sum `=2sqrt(20)=4sqrt(5)`


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