Find the radius of a circle with the equation:
x^2 + y^2 – 18x – 24y + 124 = 0
+287 Given x^2 + y^2 – 18x – 24y + 124 = 0 .
Find the radius: KEY POINTS to recognize
1) Know that the general equation of a circle is x2 + y2 +2ax +2by +C = 0.
2) The center of the circle is given by (-a, -b).
3) The radius is given by \(r= {\sqrt{a^2+b^2 -c} }\)
4) We can use radius formula above when
: the coeffitients of x2 and y2 are equal and no "xy" term.
5 Then : -18ax means (a = -18/2 =, -a = -9) and -24by (-b = -24/2 = -12), C = 124.
Answer radius \(r = {\sqrt{(-9)^2 +(-12)^2 - 124}}\)
\(r = {\sqrt{ 81+144 - 124}}\)
