Hello aspirant,

The answer will be-

Assume slope of line be m

(2,3) are fixed points

Equation of line:-

y-3=m*(x-2)

y-3=mx-2m

mx-y+3-2m=0

Foot of perpendicular from origin (0,0) is-

(2-0)/m=(y-0)/(-1)= -(0+3-2m)/{0.5^(1+m^2)}

m= -x/y

Now, mx-y+3-2m=0

(-x/y)x-y+3-2(-x/y)=0

x^2+y^2-2^x-3^y=0

Centre=(1, 3/2)

Radius= 0.5^(1^2+(3/2)^2-0) = √13/2

Diameter = 2*Radius = 2* (√13/2) = √13

Hope, it helps you.