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.
The standard for the equation of the circle can be given by (x - h)2 + (y - k)2 = r2
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 = r2
r = sqrt [(4 - 1)2 + (8 - 4)2]
r = sqrt [9 + 16]
r = sqrt (25)
r = 5