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Consider the equation x^(2)-24 x+y^(2)+36 y=-243. What is the radius of the circle in units?

Consider the equation x2−24x+y2+36y=−243 x^{2}-24 x+y^{2}+36 y=-243 . What is the radius of the circle in units?

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Find properties of circles from equations in general formright chevron icon

Full solution

Q. Consider the equation x2−24x+y2+36y=−243 x^{2}-24 x+y^{2}+36 y=-243 . What is the radius of the circle in units?
  1. Complete the square x-terms: Complete the square for the x-terms.\newlinex2−24x=(x−12)2−144x^2 - 24x = (x - 12)^2 - 144
  2. Complete the square y-terms: Complete the square for the y-terms.\newliney2+36y=(y+18)2−324y^2 + 36y = (y + 18)^2 - 324
  3. Add constants: Add the constants from completing the square to the other side of the equation.\newline(x−12)2−144+(y+18)2−324=−243(x - 12)^2 - 144 + (y + 18)^2 - 324 = -243\newline(x−12)2+(y+18)2=−243+144+324(x - 12)^2 + (y + 18)^2 = -243 + 144 + 324\newline(x−12)2+(y+18)2=225(x - 12)^2 + (y + 18)^2 = 225
  4. Identify radius squared: Identify the radius squared from the standard form of the circle equation.\newlineThe standard form is (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, where rr is the radius.\newlineHere, r2=225r^2 = 225
  5. Calculate radius: Calculate the radius by taking the square root of r2r^2.r=225r = \sqrt{225}r=15r = 15

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