Standard form of a circle
SAT glossary · Math
Definition
(x-h)^2 + (y-k)^2 = r^2 — the distance formula with the radical cleared, which is why r^2 and not r sits on the right. Two sign traps are on the page every time: (y+4)^2 means k = -4, and the radius is √(16) = 4, not 16.
Standard form of a circle in plain English
The standard form of a circle's equation, (x-h)^2+(y-k)^2=r^2, comes straight from the regular distance formula with the square root cleared away by squaring both sides — which is exactly why r^2 (not just r) sits by itself on the right side. Two sign traps show up constantly here: first, something like (y+4)^2 actually means the center's y-coordinate is k=-4 (you have to flip the sign to match the (y-k) pattern); and second, if the right side of the equation is 16, the radius is √(16)=4, NOT 16 itself — you always have to take a square root to get the actual radius.
Learn these first
Sign up free: all 157 SAT terms as flashcards, plus practice questions with full explanations →