Question

What is the general form of the equation of a circle with its center at (3,5)

and passing through the point (1,5)?

Answer 1

The general form of the equation of a circle with its center at (h,k) and passing through a point (x1,y1) is (x - h)^2 + (y - k)^2 = (x1 - h)^2 + (y1 - k)^2. Applying this to the given problem, the equation of the circle is (x - 3)^2 + (y - 5)^2 = 4.

Step-by-step explanation:

The general form of the equation of a circle with its center at (h,k) and passing through a point (x1,y1) is:

(x - h)2 + (y - k)2 = (x1 - h)2 + (y1 - k)2

Applying this to the given problem, where the center is at (3,5) and it passes through (1,5), we have:

(x - 3)2 + (y - 5)2 = (1 - 3)2 + (5 - 5)2

Simplifying this equation gives:

(x - 3)2 + (y - 5)2 = 4