[" If the circles "],[(x+a)^(2)+(y+b)^(2)=a^(2),(x+alpha)^(2)+(y+beta)^(2)=beta],[" cut orthogonally then "alpha^(2)+b^(2)=]

The circles (x + a)^(2) + (y + b)^(2) = a^(2), (x + alpha)^(2) + (y + beta)^(2) =beta ^(2) cut orthogonally if

If the curves : alpha x^(2)+betay^(2)=1 and alpha'x^(2)+beta'y^(2)=1 intersect orthogonally, prove that (alpha-alpha')beta beta'=(beta-beta')alpha alpha' .

If the curves: alphax^2 + betay^2 =1 and alpha'x^2 + beta'y^2=1 intersect orthogonally, prove that (alpha-alpha') betabeta' = (beta-beta') alphaalpha'

If a circle having centre at (alpha,beta) cut the circles x^(2)+y^(2)-2x-2y-7=0 and x^(2)+y^(2)+4x-6y-3=0 orthogonally,then |(3)/(4)alpha-(beta)/(2)| is equal to

If quad alpha sin ^ (2) x + beta cos ^ (2) x = 1, beta sin ^ (2) y + alpha cos ^ (2) y = nalpha sin ^ (2) alpha tan x = beta tan y, then (alpha ^ (2)) / (beta ^ (2)) is equal to

If (x)/(alpha)+(y)/(beta)=1 touches the circle x^(2)+y^(2)=a^(2) then point ((1)/(alpha),(1)/(beta)) lies on (a) straight line (b) circle (c) parabola (d) ellipse

A variable line ax+by+c=0 , where a, b, c are in A.P. is normal to a circle (x-alpha)^2+(y-beta)^2=gamma , which is orthogonal to circle x^2+y^2-4x-4y-1=0 .The value of alpha + beta+ gamma is equal to

A variable line ax+by+c=0 , where a, b, c are in A.P. is normal to a circle (x-alpha)^2+(y-beta)^2=gamma , which is orthogonal to circle x^2+y^2-4x-4y-1=0 .The value of alpha + beta+ gamma is equal to