Question

1. find the diameter of a circle whose equation is ( x^2 + (y - 2)^2 = 100 ).

options: 100, 10, 400, 20

Explanation:

Step1: Recall circle equation form

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Identify radius from given equation

Given the equation \(x^2 + (y - 2)^2 = 100\), we can rewrite it as \((x - 0)^2 + (y - 2)^2 = 10^2\). So, the radius \(r = 10\).

Step3: Calculate diameter from radius

The diameter \(d\) of a circle is related to the radius \(r\) by the formula \(d = 2r\). Substituting \(r = 10\), we get \(d = 2\times10 = 20\).

Answer:

20