A point P(4, k) lies on the circle with equation (x - 1)^2 + (y + 2)^2 = 34. What are the possible values of k?
Correct: A
Since the point P(4, k) lies on the circle, its coordinates must satisfy the circle's equation.
Substitute x = 4 and y = k into the equation:
(4 - 1)^2 + (k + 2)^2 = 34
(3)^2 + (k + 2)^2 = 34
9 + (k + 2)^2 = 34
(k + 2)^2 = 34 - 9
(k + 2)^2 = 25
Take the square root of both sides:
k + 2 = ±sqrt(25)
k + 2 = ±5
Two possible cases:
1) k + 2 = 5 => k = 5 - 2 => k = 3
2) k + 2 = -5 => k = -5 - 2 => k = -7
So, the possible values of k are -7 and 3.