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Find the radius of a circle with the equation:
x^2 + y^2 – 18x – 24y + 124 = 0

Jun 7, 2021

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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 + y+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 xand yare equal and no "xy"  term.

5 Then :  -18ax  means  (a = -18/2 =, -a =  -9)  and  -24by (-b = -24/2 = -12), C = 124.

Answer radius  $$r = {\sqrt{(-9)^2 +(-12)^2 - 124}}$$

$$r = {\sqrt{ 81+144 - 124}}$$

Jun 8, 2021