Question

A circle has a center that falls on the line `y = 7/8x +1` and passes through `( 5 ,8 )` and `(5 ,6 )`. What is the equation of the circle?

Answer 1

THe equation of the circle is `(x-48/7)^2+(y-7)^2=4.45`

Explanation:

Let `(a,b)` be the center of the circle
Then, `b=(7a)/8+1`
Write the equations of the circle with radiu `=r`
`(5-a)^2+(8-b)^2=r^2`
and `(5-a)^2+(6-b)^2=r^2`
`:.(5-a)^2+(8-b)^2=(5-a)^2+(6-b)^2`
So, `64-16b+b^2=36-12b+b^2`
`4b=28` `=>` `b=7`
Then `7a/8=6` `=>` `a=48/7`
then the radius is `r^2=(5-48/7)^2+(8-7)^2`
so `r^2=4.45`
Finally the equation of the circle is
`(x-48/7)^2+(y-7)^2=4.45`