Question

If $(a,b)$ is point on the circle whose center is on the x-axis and which touches the line $x+y=0$ at $(2,-2)$, then the greatest value of $a$ is

• A. $4+2\sqrt{2}$
• B. $2+2\sqrt{2}$
• C. $4+\sqrt{2}$
• D. None of these

Answer 1

Answer: (A)

$4+2\sqrt{2}$

Since the slope of the given line is $-1,$

$\therefore \angle COP={45}^0$

$\therefore OP=2\sqrt{2}=CP$

$\therefore OC=\sqrt{{\left(2\sqrt{2}\right)}^2+{\left(2\sqrt{2}\right)}^2}=4$

The point on the circle with the greatest x-coordinate is $A.$

$\therefore a=OA=OC+CA=4+2\sqrt{2}.$