Circles `|z-1| = 3, |z-z_0| = 4` intersect orthogonally, then

If the circle |z-1|=3 and |z-z_(0)|=4 intersect orthogonally,then

Prove that the circles z bar z +z( bar a _1)+bar z( a_1 )+b_1=0 ,b_1 in R and z bar z +z( bar a _2)+ bar z a_2+b_2=0, b_2 in R will intersect orthogonally if 2R e(a_1 bar a _2)=b_1+b_2dot

Prove that the circles z bar z +z( bar a )_1+bar z( a )_1+b_1=0 ,b_1 in R and z bar z +z( bar a )_2+ bar z a_2+b_2=0, b_2 in R will intersect orthogonally if 2R e(a_1( bar a )_2)=b_1+b_2dot

Prove that the circles z bar z +z( bar a _1)+bar z( a_1 )+b_1=0 ,b_1 in R and z bar z +z( bar a _2)+ bar z a_2+b_2=0, b_2 in R will intersect orthogonally if 2R e(a_1 bar a _2)=b_1+b_2dot

If the tangents at z_(1) , z_(2) on the circle |z-z_(0)|=r intersect at z_(3) , then ((z_(3)-z_(1))(z_(0)-z_(2)))/((z_(0)-z_(1))(z_(3)-z_(2))) equals

If the tangents at z_(1) , z_(2) on the circle |z-z_(0)|=r intersect at z_(3) , then ((z_(3)-z_(1))(z_(0)-z_(2)))/((z_(0)-z_(1))(z_(3)-z_(2))) equals

If the tangents at z_(1) , z_(2) on the circle |z-z_(0)|=r intersect at z_(3) , then ((z_(3)-z_(1))(z_(0)-z_(2)))/((z_(0)-z_(1))(z_(3)-z_(2))) equals

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.