Use the information provided to write the standard form equation of each circle Center (1, 2) points on Circle (10, 1)

Solution:

By definition, a circle of radius ‘a’ is the set of all points P(x, y) whose distance from the center C(h, k) equals ‘a’ (Figure below).

From the distance formula, P lies on the circle if and only if

√(x - h)² + (y - k)² = a

Or

(x - h)² + (y - k)² = a²

In the problem given above the centre is C(1, 2)

h = 1, k = 2

And the point is P(10, 1)

x = 10, y = 1

The radius of the circle is therefore:

a = √(10 - 1)² + (1 - 2)²

a = √9² + (-1)²

a = √(81 + 1)

a = √82

The standard equation of the circle is :

(x - 1)² + (y - 2)² = (√82)²

(x - 1)² + (y - 2)² = 82

Use the information provided to write the standard form equation of each circle Center (1, 2) points on Circle (10, 1)

Summary:

The standard form equation of each circle Center (1, 2) points on Circle (10, 1) is (x - 1)² + (y - 2)² = 82