A circle has a center that falls on the line #y = 11/7x +8 # and passes through # ( 9 ,1 )# and #(8 ,7 )#. What is the equation of the circle?
2 Answers
Explanation:
We will make two equations with two variables, where
The first equation is the given line, which passes through the center of the circle. Isolate
We know that the points
Substitute
The exact answers can be found by squaring each side, then expanding the polynomials to get a quadratic equation, but only one of the values for
(Using a graphing calculator)
Now plug these in to the standard form for the equation of a circle to get:
Explanation:
Centre falls on
as points
Observe that the slope of this segment is
As their midpoint point is
and centre is point of intersection of
i.e.
or
and
and centre is
and equation of circle is
graph{((x+455/118)^2+(y-229/118)^2-(9+455/118)^2+(1-229/118)^2)(y-11/7x-8)((x-9)^2+(y-1)^2-0.04)((x-8)^2+(y-7)^2-0.04)(y-1/6x-31/12)=0 [-20.92, 19.08, -8.88, 11.12]}