Circle : Equation of Circle , Equation of Circle in different cases , Position of a Point with respect to circle.
Equation of Circle
Let C(i, j) be the centre of the circle and CP(r) be the radius of the Circle, then the equation of the circle is
Now, origin (0, 0) be the centre of the circle then equation 1 becomes,
The area of the circle is given by
General Equation of Circle
The General equation of the second degree may represent a circle if the coeffcient of and coeffcient of
are identical and coeffcient of xy becomes zero i.e
represents a circle if a =b i.e
then equation 1 reduces as
whose centre and radius are
Equation of circle in diameter form
Let
be the end points of a diameter of the given circle and let P(x,y) be any point on the circle such that
Slope of AP
for a perpendicular, m1 * m2 = 1 i.e AP * BP = -1
Equation of Circle in different cases
Case 1:
When circle passes through origin (0,0). let the equation of the circle be
it passes through origin (0,0)
equation 1 becomes
Case 2:
When circle passes through x- axis. let the centre of the circle be C(i, j) and toches x-axis at point P , then radius of the circle is
equation of the circle
Case 3:
When circle passes through y- axis. let the centre of the circle be C(i, j) and toches y-axis at point P , then radius of the circle is
equation of the circle
Case 4:
When circle toches both axis. In this case
then equation of the circle