Q. The centres of three circles $x^{2} + y^{2} = 1,\ x^{2} + y^{2} + 6x - 2y = 1,\ x^{2} + y^{2} - 12x + 4y = 1$ are
A) Collinear
B) Non-collinear
C) Nothing to be said
D) None of these
Explanation
(a)
The centre of given circles are $C_{1}(0,\ 0),\ C_{2}( - 3,\ 1)$ and $C_{3}(6,\ - 2)$
Now, $\left| \begin{matrix}
0 & 0 & 1 \\
- 3 & 1 & 1 \\
6 & - 2 & 1
\end{matrix} \right| = 1(6 - 6) = 0$
Hence, centres are collinear
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.