Example Question - finding diameter

Finding the Diameter of a Circle from a Given Equation

Complete the square for \( x \) and \( y \): \( x^2 + 22x = x^2 + 22x + (22/2)^2 - (22/2)^2 = (x+11)^2 - 121 \) \( y^2 + 30y = y^2 + 30y + (30/2)^2 - (30/2)^2 = (y+15)^2 - 225 \) Rewrite the equation: \( (x+11)^2 - 121 + (y+15)^2 - 225 + 90 = 0 \) \( (x+11)^2 + (y+15)^2 = 121 + 225 - 90 \) \( (x+11)^2 + (y+15)^2 = 256 \) The equation \( (x+11)^2 + (y+15)^2 = 256 \) represents a circle with radius \( r^2 = 256 \), so \( r = 16 \). Diameter \( d = 2r = 2 \times 16 = 32 \). The diameter of the circle is 32.