A circle has a center that falls on the line #y = 7/9x +7 # and passes through # ( 4 ,5 )# and #(8 ,1 )#. What is the equation of the circle?
1 Answer
The equation of the circle is
Explanation:
The mid point of
The slope of the line through
The slope of the line perpendicular to the line through
The equation of the line through
The center of the circle lies on the intersection of lines
and
Therefore,
and
So,
The center of the circle is
The radius is
The equation of the circle is
graph{((x-4)^2+(y-5)^2-1/16)((x-8)^2+(y-1)^2-1/16)(y-x+3)(y-7/9x-7)(x+y-9)=0 [-8.75, 21.25, -4.1, 10.9]}
graph{((x-45)^2+(y-42)^2-3050)(y-x+3)(y-7/9x-7)=0 [-90, 150, -20, 100]}