CBSE Class 11-science Answered
Circle of radius a and diameter on x axis.
y = mx is the chord.
The first point is origin for the chord at the other point y = mx, but this point is also on the circle,
x2 + y2 = a2
x2 + m2x2 = a2
x = ±a/(1 + m2)
For the circle with diameter as the chord, the center will be at (x/2, mx/2) since the two end points of the chord are (0,0) and (x. mx/2)
and radius2, ((x/2)2 + (mx/2)2) = ((x2 + m2x2)/4) = a2/4
Hence the equation of the circle,
(x - (a/(1 + m2))2 + (y - a/(1 + m2))2 = a2/4
)2 + y2 = a2