A circle has a center that falls on the line #y = 7/2x +3 # and passes through #(1 ,2 )# and #(8 ,1 )#. What is the equation of the circle?
1 Answer
Explanation:
Point A
This is lies on the line of points (L) that are all equi-distant from A and B
the formula for calculating the distance (d) between two points (from pythagorus) is
substitute in what we know for point A and an arbitrary point on L
substitute in what we know for point B and an arbitrary point on L
Therefore
Expand the brackets
Simplify
the centre point lies on the line
and on the line
solve where these two lines cross to find the centre of the circle
substitute into
The centre of the circle is at
the squared radius of the circle can now be calculated as
The general formula for a circle or radius
We now know
expand the brackets
and simplify