Question

If the point \( (2, k) \) lies on the circle \( (x - 2)^2 + (y + 1)^2 = 4 \), then the value of \( k \) is:

• A. \( 1, 3 \)
• B. \( 1, 2 \)
• C. \( -1, 3 \)
• D. \( 2, 3 \)
• E. \( 1, -3 \)

Hint:

When a point lies on a circle, substitute the coordinates of the point into the equation of the circle to solve for the unknown.

Answer 1

Answer: (E)

Substitute the point \( (2, k) \) into the equation of the circle: \[ (2 - 2)^2 + (k + 1)^2 = 4 \] This simplifies to: \[ (k + 1)^2 = 4 \] Taking the square root of both sides: \[ k + 1 = \pm 2 \] Thus, \( k = 1 \) or \( k = -3 \).