Question

The locus of the center of the circle for which one end of the diameter is $(3,3)$ while the other end lies on the line $x+y=4$ is

• A. $x+y=3$
• B. $x+y=5$
• C. $x+y=7$
• D. $x+y=9$

Answer 1

Answer: (B)

$x+y=5$

Let locus of the point center b $(h,k)$.

Any point on the line $x+y=4$

can be taken as $(a,4-a)$

$h=\frac{3+a}{2}$

$k=\frac{3+(4-a)}{2}=\frac{7-a}{2}$

$2h-a-3=-(2k-7+a)$

$2h-a-3=-2k+7-a$

$2h+2k=10$

$h+k=5$

Put $h=x$ $k=y$

$x+y=5$

Option B is correct