An equation of circle of radius 'r' with a center in a point is:
If a center of the circle coincides with the origin of coordinates, then an equation of circle is:
An equation which can be written in the following form represents a circle except when
D2 + E2 ≤ F
This is called the general form of the circle .
is the centre of the circle and the radius is
Find the radius and centre of the circle x2 + y2 - 2x - 4y + 1 = 0
We need to get the equation into the form:
The radius of circle is r = 2 and the centre of the circle is O(1, 2).
In this example D = -1, E = 2, F = 1
Find the equation of the circle through the points A(4, -2), B(6, 1), C(-1, 3).
Let represent the circle. Then, since A is on the circle, its coordinates, 4 and -2, satisfy the equation
Whence: 8D - 4E + F = -20.
Similary, for B, 12D + 2E + F = -37.
and for C, -2D + 6E + F = -10.
Solving, we have , and the equation is:
Let A(x1, y1) be a point of the circle (x - a)2 + (y - b)2 = r2 , then an equation of tangent line to circle is:
Given the circle (x - 1)2 + (y - 2)2 = 25 and the point A(4,6) on the circle. Find the equation of the tangent to the circle at A.
Here we have: a = 1, b = 2, x1 = 4, y1 = 6
The equation of tangent is: