# Write the equation of a circle with a center at (1, 4) where a point on the circle is (4, 8).

The standard form of the equation can be written with the help of center coordinates and radius of the circle, only.

## Answer: The equation of the circle will be (x - 1)^{2} + (y - 4)^{2} = 25

The radius of the circle is the distance between the center and any of the coordinates that lie on its circumference.

**Explanation:**

The standard for the equation of the circle can be given by (x - h)^{2} + (y - k)^{2} = r^{2}

Here, (h, k) are the coordinates of the center.

We will find the value of r by substituting the value of center in this equation.

h = 1, k = 4, r = ?

To calculate r, we need the calculate the distance between the center and any point lying on the circumference of the circle.

(4 - 1)^{2} + (8 - 4)^{2} = r^{2}

r = sqrt [(4 - 1)^{2} + (8 - 4)^{2}]

r = sqrt [9 + 16]

r = sqrt (25)

r = 5