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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»


SOLUTION :`(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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