A circle has a center that falls on the line y = 7/4x +4 and passes through ( 4 ,7 ) and (7 ,5 ). What is the equation of the circle?
1 Answer
2x^2 + 2y^2 + 100x + 159y - 1643 = 0
Explanation:
General equation of circle can be represented as
where
As we know the given points
Putting the given points
=>
8h + 14k - c = 65 ->Equation 2
=>
14h + 10k - c=74 ->Equation 3
Since the centre of the circle is
7h - 4k = -16 ->Equation 4
Subtract Equation 2 and 3
=>
6h -4k = 9 ->Equation 5
Add Equation 4 and 5
=>
-h = 25 => h= -25
-4k= 9 - (6*(-25)
k = -159/4
Solving for c in Equation 3, we get
c= -3286/4 =-1643/2
Circle equation is:
x^2+y^2+50x-(-159/2)y - 1643/2=0
2x^2 + 2y^2 + 100x + 159y - 1643 = 0