Q. Equation of the circle passing through the point (3, 4) and concentric with the circle $x^{2} + y^{2} - 2x - 4y + 1 = 0$ is
A) $x^{2} + y^{2} - 2x - 4y = 0$
B) $x^{2} + y^{2} - 2x - 4y + 3 = 0$
C) $x^{2} + y^{2} - 2x - 4y - 3 = 0$
D) None of the above
Explanation
(c)
Let the equation of the centric circles be $x^{2} + y^{2} - 2x - 4y + \lambda = 0$, it passes through (3, 4)
$\therefore 3^{2} + 4^{2} - 2(3) - 4(4) + \lambda = 0$
$\Rightarrow \ \lambda = - 3$
Thus, the equation of concentric circle is
$x^{2} + y^{2} - 2x - 4y - 3 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.