A circle has a center that falls on the line y = 1/7x +4 and passes through ( 7 ,8 ) and (3 ,6 ). What is the equation of the circle?

1 Answer
Somebody N.
Apr 23, 2018

color(blue)((x-91/15)^2+(y-73/15)^2=481/45)

Explanation:

The equation of a circle is given by:

(x-h)^2+(y-k)^2=r^2

Where (h,k) are the x and y coordinates of the centre respectively and r is the radius.

The centre lie on the line y=1/7x+4

:.

k=1/7h+4 \ \ \ \ \ \ [1]

(7,8) and (3,6) lie on the circle:

(7-h)^2+(8-k)^2=r^2 \ \ \ \ \ \ [2]

(3-h)^2+(6-k)^2=r^2 \ \ \ \ \ \ [3]

Subtract [3] from [2]

68-8h-4k=0

Substituting k=1/7h+4

68-8h-4(1/7h+4)=0

52-60/7h=0=>h=91/15

Substituting in [1]:

k=1/7(91/15)+4

k=73/15

We now need the value of r^2

Using coordinate (3,6)

(3-91/15)^2+(6-73/15)^2=r^2

r^2=481/45

So the equation of the circle is:

color(blue)((x-91/15)^2+(y-73/15)^2=481/45)

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