A circle has a center that falls on the line #y = 7/8x +1 # and passes through # ( 5 ,2 )# and #(3 ,6 )#. What is the equation of the circle?
2 Answers
The equation of the circle is
Explanation:
Let
The slope of
The slope of the line perpendicular to
The equation of the line passing trrough
The intersection of this line with the line
The center of the circle is
The radius of the circle is
The equation of the circle is
graph{((x-8/3)^2+(y-10/3)^2-65/9)(y-7/8x-1)(y-1/2x-2)=0 [-9, 11, -1.96, 8.04]}
Explanation:
Let the equation of circle be
As the centre is on
or
It also passes through
Subtracting (2) from (3), we get
Adding (1) and (4), we have
and puuting this in (1), we get
Hence
i.e.
Hence, equaton of circle is
or
graph{(3x^2+3y^2-16x-20y+33)((x-5)^2+(y-2)^2-0.01)((x-3)^2+(y-6)^2-0.01)(y-(7x)/8-1)=0 [-7.83, 12.17, -1.94, 8.06]}