Q. The locus of the centre of the circle for which one end of a diameter is (1, 1) while the other end is on the line $x + y = 3$, is
A) $x + y = 1$
B) $2(x - y) = 5$
C) $2x + 2y = 5$
D) None of these
Explanation
(c)
Let the centre of circle be$(g,\ f)$. If one end of a diameter is (1, 1), then the other end of a diameter is $(2g - 1,\ 2f - 1)$
Since, this end is lie on the line $x + y = 3$
$\Rightarrow \ \ \ 2g - 1 + 2f - 1 = 30$
$\Rightarrow \ \ 2g + 2f = 5$
$\therefore$ Locus of centre of circle is $2x + 2y = 5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.