Question

The equation of a circle is $C : x^2 + y^2 - 6 x - 4y + 11 = 0$ . $A$ point $P(4,3)$ that lies on this circle is taken. $A$ diameter with $P$ as an end is drawn. What will be the coordinates of its other end?

• A. $(2,1)$
• B. $(4, 3)$
• C. $(5,4)$
• D. $(1, 3)$

Answer 1

Answer: (A)

$(2,1)$

Answer 2

The correct option is(A): (2,1)

Given equation of circle is
$x^{2}+y^{2}-6x-4y+11=0$
Its centre is $O(3, 2)$.
Given that $P(4, 3)$ is an end of diameter
Let $Q(x,y)$ be the other end of diameter
So, centre $O(3, 2)$ is the mid-point of $PQ$
$\therefore 3=\frac{4+x}{2}$ and $2=\frac{3+y}{2}$
$\Rightarrow x=2$ and $y=1$
So, $Q(2, 1)$ is the other end of diameter.