looking at the question where to circles are drawn through (1,5) and (4,1) and touch the y axis i think it can be done like this assume a general equation of a circle as x^2+y^2+2gx+2fy+c=0 now if we make it satisfy the points given to us we get to equation and three variables but both these circles satisfy the condition that they touch the y- axis hence when we put x=0 we get a quadratic in y that has a single root and hence b^2=4ac from this condition we get g^2=c or g=+or-c hence we get to circles now with g=c and g=-c now once eqation of circles has been found out you can easily deffrentiate and find the angle subtende at the point of intersection please correct me if i am wrong and nudge me if you have any doubts
Moderation Team
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