Question

Let P(a,b) be a point in the first quadrant, circles are drawn through P touching the coordinate axes such that the circles are orthogonal thrn a^2+b^2=kab then find value of k.

Answer 1

Does this mean a and b are the diameters of the circles?

Answer 2

Two circles are orthogonal only if the respective tangents in a point of intersection are perpendicular to each other.
We can further it out by saying that the radiuses of both circles that include the point of intersection, must be perpendicular.

Answer 3

can you please help a little more in this?

Answer 4

i got these equations x^2+y^2+2g1x+2f1y+c1=0
and x^2+y^2+2g2x+2f2y+c2=0
2g1g2+2f1f2=c1+c2
r2=f2,r1=g1

Answer 5

\[(g1-g2)\alpha+(f1-f2)\beta=f1f2+g1g2-c1\]
\[(g2-g1)\alpha+(f2-f1)\beta=f1f2+g1g2-c2\]