The middle term in the expansion of is




using the property of H.M
multiplying the above equations, we get
now dividing by bc,
Let us take the coordinates as (-4,3), (2,-3) and (0,p).
If the points are collienear the |x1(y2 - y3) + x2(y3 - y1) + x3(y1-y2)| = 0
Now substituting the values |-4(-3 - p) +2(p -3) +0(3+3)|= 0
12 +4p +2p -6 +0 = 0
6p +6 = 0
6p = -6
Therefore p = -1
The line y = m x + c is a normal to the circle
has center (-g,-f)
As normal passes through center so center will satisfy the equation of normal
put y=-f and x=-g in equation of the line y=mx+c
-f = m(-g) +c
which gives mg =f+c.
