Prove that the circle `zbarz+zbara_1+barza_1+b_1=0; b_1inRR` and `zbarz+zbara_2+barza_2+b_2=0, b_2inRR` will intersect orthogonally if `2Re(a_1bara_2)=b_1+b_2`.

Prove that the circles zbar(z)+z(bar(a))_(1)+bar(z)(a)_(1)+b_(1)=0,b_(1)in R and zbar(z)+z(bar(a))_(2)+bar(z)a_(2)+b_(2)k=0,b+2in R will intersect orthogonally if 2Re(a_(1)(bar(a))_(2))=b_(1)+b_(2)

The curves ax^(2)+by^(2)=1 and Ax^(2)+B y^(2) =1 intersect orthogonally, then

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

Find the condition for the two concentric ellipses a_(1)x^(2)+b_(1)y^(2)=1 and a_(2)x^(2)+b_(2)y^(2)=1 to intersect orthogonally.

Show that the circle passing through the origin and cutting the circles x^2+y^2-2a_1x-2b_1y+c_1=0 and x^2+y^2-2a_2x -2b_2y+c_2=0 orthogonally is |(x^2+y^2,x,y),(c_1,a_1,b_1),(c_2,a_2,b_2)|=0

If the line a_1 x + b_1 y+ c_1 = 0 and a_2 x + b_2 y + c_2 = 0 cut the coordinate axes in concyclic points, prove that : a_1 a_2 = b_1 b_2 .

If the points (a_1, b_1),\ \ (a_2, b_2) and (a_1+a_2,\ b_1+b_2) are collinear, show that a_1b_2=a_2b_1 .

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

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally