Algebra

Let us put a circle of radius 5 on a graph. Now let's work out exactly where all the points are.

We make a right-angled triangle: 52+ 02= 25 + 0 = 253432+ 42= 9 + 16 = 250502+ 52= 0 + 25 = 25−4−3(−4)2+ (−3)2= 16 + 9 = 250−502+ (−5)2= 0 + 25 = 25

Start with:x2 + y2 = r2

Values we know:22 + y2 = 52

Rearrange:y2 = 52 − 22

Square root both sides:y = ±√(52 − 22)

Solve:y = ±√21

y ≈ ±4.58...