- #1
Saitama
- 4,243
- 93
Homework Statement
Consider a family of circles passing through two fixed points A(3,7) and B(6,5). Show that the chords in which the circle ##x^2+y^2-4x-6y-3=0## cuts the members of the family are concurrent at a point. Find the coordinates of this point.
Homework Equations
The Attempt at a Solution
The family of circles passing through the two given points is given by:
$$(x-1)(x-6)+(y-7)(y-5)+\lambda \left|
\begin{array}{c c c}
x & y & 1\\
3 & 7 & 1\\
6 & 5 & 1\\
\end{array}
\right|=0$$
I am completely clueless about the next step.
Any help is appreciated. Thanks!