If the center of the circle were moved from the origin to the point h comma k and point P at x comma y remains on the edge of the circle, which could represent the equation of the new circle?
Answer
A
open paren h plus x close paren squared plus open paren k plus y close paren squared is equal to r squared
B
open paren x minus k close paren squared plus open paren y minus h close paren squared is equal to r squared
C
open paren k plus x close paren squared plus open paren h plus y close paren squared is equal to r squared
D
open paren x minus h close paren squared plus open paren y minus k close paren squared is equal to r squared
Explanation
A circle with center (h, k) and radius r has equation (x − h)² + (y − k)² = r². Since P = (x, y) lies on the circle, its horizontal and vertical distances from the center are x − h and y − k. This matches choice D.
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