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#