The length of the diameter of the circle which touches the X axis at the point (1,0) and passes through the point (2,3) is ?
Solution) If a circle touches the x-axis, its equation is
(x-h)^2+(y-k)^2=k^2
but it is given that the equation passes thru the point (1,0)
=> 1+h^2-2h=0
=> h=1,0
and also that tha equation passes thru the point (2,3)
=> 4+9-4h-6k+h^2=0
=> 13-4-6k+1=0
=> k=5/3=radius
diameter = 2(radius)= 10/3