# 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#