If a circle have an equation of circle :

And a line have an equation of line :

x2 + y2 + Ax + By + C = 0

Y = mx + n

Suppose that a line with equation of line y = mx + n and

a circle with equation of x2 + y2 + Ax + By + C = 0 , then substitute the line’s equation into the circle’s equation

to produce a new equation in the form of quadratic equation like above :

x2 + (mx + n)2 + Ax + B (mx + n) + C = 0 x2 + (m2 x2 + 2mnx + n2) + Ax + Bmx +Bn + C = 0

x2 + m2 x2 + 2mnx + Ax + Bmx + n2 + Bn + C = 0 (1 + m2) x2 + (2mn + A + Bm)x + n2 + Bn + C = 0

Atau(1 + m2) x2 + (A + 2mn + Bm)x + n2 + Bn + C = 0

So , we can determine the simple form of the quadratic equation like above :

And the value of discriminant is :

ax2 + bx + c = 0

D = b2 – 4 . a . c , According to above des cription the

’ requirement re lated to particular line s pos ition :toward c irc le could be expres s as follow

2. > 0 , If D s o the line and circ le have two inters ection points

3. = 0 , If D s o the line and circ le have one inters ection point

4. < 0 , If D s o the line and circ le have no inters ection point

The line and circle have two

intersection points

The line and circle have an

exactly one intersection

point

The line and circle have no intersection

point