Question

The equation of the circle of radius 2Ц2 whose centre lies on the line x – y = 0 and which touches the line x + y = 4, and whose centre's coordinates satisfy the inequality x + y > 4 is

• A. x2 + y2 – 8x – 8y + 24 = 0
• B. x2 + y2 = 8
• C. x2 + y2 – 8x – 8y = 24
• D. None of these

Answer 1

Answer: (A)

x2 + y2 – 8x – 8y + 24 = 0

Answer 2

Let centre is (h, h)

$\frac{h + h - 4}{\sqrt{2}}$= 2$\sqrt{2}$

Ю 2h = 8 Ю h = 4, centre = (4, 4)