01:640:111 Lecture 4: 10_5 Precalc Lecture

• School: Rutgers University
• Department: Mathematics
• Course: 01:640:111
• Professor: Threlfall

Document Summary

Equation of circle with center (a,b) and radius r ( a a + ( b 2 = r2 x y. Only a circle if the number associated with x and y are one, and there is no higher power than 2. Example: x2 + y2 + 4 6 + 1 = 0. Step 1: isolate the constant (on the r-side) 2 y x x2 + y2 + 4 6 = 1 y 2 x x. Step 2: collect the x-terms and collect the y-terms. Step 3: complete the square ( 2 + 4 + 4 + ( 2 6 + 9 = 1 + 4 + 9 x y ( + 2 2 + ( 3)2 = 1 x. Center is opposite of what you see: (-2,3) The radius is the square root of the constant on the right: 1. Example: x2 + y2 + 2 6 + 9 x y.