Question

What are the x-intercepts of the circle (x – 3)2 + (y – 4)2 = 24?

Answer 1

X-intercept ⇒ When y = 0

(x – 3)² + (y – 4)² = 24

When y = 0,
(x – 3)² + (0 – 4)² = 24

(x – 3)² + 16 = 24

(x – 3)² = 8

(x - 3) = ±√8

x = √8 + 3 or x = -√8 + 3 

x = (3 + 2√2) or (3- 2√2)        [Radical Form]

x = 5.83 or 0.17                     [Decimal Form]

Answer: (5.83, 0) and (0.17, 0)

Answer 2

(x-3)2+(y-4)2=24
2x-6+2y=24
2x-14+2y=24
2x=24+14-2y
2x=38-2y
x=19-y