Q. Circle $x^{2} + y^{2} - 2x - \lambda x - 1 = 0$ passes through two fixed points coordinates of the points are
A) $(0,\ \pm 1)$
B) $( \pm 1,\ 0)$
C) (0, 1) and (0, 2)
D) $(0,\ - 1)\ and\ (0,\ - 2)$
Explanation
(a)
$\left( x^{2} + y^{2} - 2x - 1 \right) + \lambda x = 0$, they pass through intersection points of line $x = 0$ and circle $x^{2} + y^{2} - 2x - 1 = 0$
$\Rightarrow y = \pm 1$
$\therefore$ Required points are $(0,\ \pm 1)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.