Question

Equation of the circle with centre $(-3, 2)$ and radius 4 is

• A. $(x+3)^2 + (y+2)^2 = 4^2$
• B. $(x-3)^2 + (y+2)^2 = 16$
• C. $(x+3)^2 + (y-2)^2 = 16$
• D. $(x-2) + (y+3)^2 = 4^2$

Hint:

Be extremely careful with the signs. The formula has negative signs ($x-h$), so a negative coordinate like $-3$ becomes $(x - (-3)) = (x+3)$. Always "flip" the sign of the centre coordinates when putting them into the parentheses.

Answer 1

The Correct Option is C

1. Standard Form Equation: The equation of a circle with centre $(h, k)$ and radius $r$ is: $$(x - h)^2 + (y - k)^2 = r^2$$

2. Substitution: Given: Centre $(h, k) = (-3, 2)$ Radius $r = 4$ Substituting these into the formula: $$(x - (-3))^2 + (y - 2)^2 = 4^2$$ $$(x + 3)^2 + (y - 2)^2 = 16$$ This matches Option (C). Options (A) and (B) have incorrect signs for the $y$ or $x$ components respectively.