Question

17.1 equation of a circle
example #3
determine the diameter of the circle with the equation
$(x - 3)^2 + (y - 5)^2 = 49$.
to be graded
how did you find the diameter of the circle given
the equation?
the radius
need to ask or add anything?
rewatch
continue

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 \(r^2\) from given equation

Given \((x - 3)^2 + (y - 5)^2 = 49\), we see \(r^2 = 49\).

Step3: Solve for radius \(r\)

Take the square root: \(r = \sqrt{49} = 7\).

Step4: Calculate diameter (d = 2r)

Diameter \(d = 2\times7 = 14\).

Answer:

The diameter of the circle is 14. To find it, first identify the radius from the circle's equation \((x - 3)^2 + (y - 5)^2 = 49\) (since the standard form is \((x - h)^2 + (y - k)^2 = r^2\), \(r^2 = 49\) means \(r = 7\)), then multiply the radius by 2 (diameter \(= 2r\), so \(2\times7 = 14\)).