Question

a circle passes through (0,0), (a,0) and (0,b) then what is trhe center of circle

Answer 1

Answer:

Step-by-step explanation:

equation of circle assuming a,0 and 0,b as diametric end points

x(x-a)+y(y-b) = 0

equation of diameter joining a,0 and 0,b

bx+ay=ab

by family of circles

x(x-a)+y(y-b) + lamda(bx+ay-ab) = 0

as 0,0 satisfies above equation

-a-b+lamda(-ab)

lamda = a+b / -ab

x(x-a)+y(y-b)+ a+b / -ab (bx+ay-ab) = 0

expanding you get equation of circle and you find center