Question

17.1 equation of a circle
example #3
determine the diameter of the circle with the equation
$(x - 3)^2 + (y - 5)^2 = 49$.
multiple-choice question
what is the diameter of this circle?
14
49
7
rewatch

Explanation:

Step1: Recall circle equation form

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

Step2: Identify radius from given equation

Given \((x - 3)^2 + (y - 5)^2 = 49\), we compare with the standard form. Here, \(r^2 = 49\), so \(r=\sqrt{49}=7\).

Step3: Calculate diameter

Diameter \(d = 2r\). Substituting \(r = 7\), we get \(d = 2\times7 = 14\).

Answer:

14