find the equation of the circle drawn on the intercept made by the line 3x+4y=12 between the coordinate axes as diameter

Hello Achyus, same way try to draw figure with points got on x axis and y axis as A(4,0) and B(0.3)
As AB has to be the diameter, its mid point i.e (2, 3/2) is the centre. Radius = diameter AB/2
Radius = √[(3^2 + 4^2)] /2 = 5/2
So equation of circle 
(x - 2)^2 + (y - 3/2)^2 = 25/4
 

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