Max. and Min. in Circle

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\hspace{-16}$Let $\mathbf{(x,y)}$ be Real variables Satisfying $\mathbf{x^2+y^2+8x-10y-40=0}$\\\\ If $\mathbf{a=Max\{(x+2)^2+(y-3)^2\}}$ and $\mathbf{b=Min\{(x+2)^2+(y-3)^2\}}$\\\\ Then find\\\\ (i)\;\; $\mathbf{a+b=}$\\\\ (ii)\;\; $\mathbf{a-b=}$\\\\ (iii)\;\; $\mathbf{a.b=}$\\\\

#Mathematics #Algebra

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Aditya Bhutra ·2012-03-13 12:01:07

(x,y) represents any point on the given circle.

a = square of maximum distance of a point on the circle and (-2,3)
= Radius + distance between center and point(-2,3) = 9+2âˆš2

b=square of minimum distance of a point on the circle and (-2,3)
= Radius - distance between center and point(-2,3) = 9 - 2âˆš2

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