if y=mx be the equation of the chord of the circle x2 +y2 -2ax=0 ,then find the equaiton of the circle of which this chord is the diameter?
62(x-a)2+(y)2=a2
y=mx
x2(1+m2)-2ax=0
sum of roots is 2a/(1+m2)
one root is zero
so the other x where it cuts the circle is 2a/(1+m2) and y is mx thus 2am/(1+m2)
the equation of the circle with the end point as diameter is known.. you can solve itnow :)
1one more method is finding the two points of intersection of given circle and chord and then finding the midpoint of that chord, this mid point will be the centre of the new circle , then we can find the equation as we know the centre of the circle
