" If the circles "x^(2)+y^(2)+2a^(2)x+2b^(1)y+c^(1)=0" and "2x^(2)+2y^(2)+2ax+2by+c=0" intersect orthogonally,then "

If the circles x^2+y^2+2a^(prime)x+2b^(prime)y+c^(prime)=0 and 2x^2+2y^2+2a x+2b y+c=0 intersect othrogonally, then prove that a a^(prime) + b b prime=c+c^(prime)/2dot

If the circles x^2+y^2+2a^(prime)x+2b^(prime)y+c^(prime)=0 and 2x^2+2y^2+2a x+2b y+c=0 intersect othrogonally, then prove that a a^(prime) + b b prime=c+c^(prime)/2dot

If the circles x^(2)+y^(2)+2a'x+2b'y+c'=0 and 2x^(2)+2y^(2)+2ax+2by+c=0 intersect othrogonally,then prove that aa'+bbquad =c+(c')/(2)

If the circles x ^(2) + y ^(2) + 5x -6y-1=0 and x ^(2) + y^(2) +ax -y +1=0 intersect orthogonally (the tangents at the point of intersection of the circles are at right angles), the value of a is

If the circles x ^(2) + y ^(2) - 8x - 6y + c= 0 and x ^(2) + y ^(2) - 2y + d =0 cut orthogonally, then c + d equals

If the curves (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 intersect orthogonally, then

If the curves (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 intersect orthogonally, then

Show that the circle passing through the origin and cutting the circles x^(2)+y^(2)-2a_(1)x-2b_(1)y+c_(1)=0 and x^(2)+y^(2)-2a_(2)x-2b_(2)y+c_(2)=0 orthogonally is det[[c_(1),a_(1),b_(2)c_(1),a_(1),b_(2)c_(2),a_(2),b_(2)]]=0

If the curve ax^(2)+by^(2)=1 and a'x^(2)+b'y^(2)=1 intersect orthogonally, then