Question

what is the diameter of the circle described by the equation (x + 2)^2+(y - 5)^2-225 = 0?
a 225
b 30
c 60
d 450

Explanation:

Step1: Rewrite the circle - equation in standard form

The standard form of a circle equation is \((x - a)^2+(y - b)^2=r^2\), where \((a,b)\) is the center of the circle and \(r\) is the radius. Given \((x + 2)^2+(y - 5)^2-225 = 0\), we can rewrite it as \((x+2)^2+(y - 5)^2=225\).

Step2: Identify the radius

Comparing \((x + 2)^2+(y - 5)^2=225\) with \((x - a)^2+(y - b)^2=r^2\), we have \(r^2 = 225\). Taking the square - root of both sides, \(r=\sqrt{225}=15\) (we take the positive value since \(r\) represents the radius of a circle).

Step3: Calculate the diameter

The diameter \(d\) of a circle is related to the radius by the formula \(d = 2r\). Substituting \(r = 15\) into the formula, we get \(d=2\times15 = 30\).

Answer:

B. 30