The point (6, 5) lies on a circle centered at (3, -2). Find the radius of the circle.

Solution:

The standard form of the equation of a circle is given by

(x - a)² + (y - b)² = r²

Where a and b are the coordinates of the center

r is the radius

Given, center = (3, -2) and (x, y) = (6,5)

Substituting the values in standard form of equation we get,

(6 - 3)² + (5 - (-2))² = r²

(3)² + (7)² = r²

r² = 9 + 49

r = √58

Therefore, the radius of the circle is √58.

The point (6, 5) lies on a circle centered at (3, -2). Find the radius of the circle.

Summary:

The point (6, 5) lies on a circle centered at (3, -2). The radius of the circle is √58.