A circle has a center that falls on the line y = 8/9x +7 y=89x+7 and passes through ( 4 ,1 )(4,1) and (3 ,7 )(3,7). What is the equation of the circle?

1 Answer
Somebody N.
May 15, 2018

color(blue)((x+129/26)^2+(y-101/39)^2=503977/6084)(x+12926)2+(y−10139)2=5039776084

Explanation:

The general equation of a circles is:

(x-h)^2+(y-k)^2=r^2(x−h)2+(y−k)2=r2

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

So (h,k)(h,k) are on the line y=8/9x+7y=89x+7

Substituting hh and kk:

k=8/9h+7 \ \ \ \ \ [1]

(4,1) lie on the circumference:

(4-h)^2+(1-k)^2=r^2 \ \ \ \ [2]

(3,7) lie on the circumference:

(3-h)^2+(7-k)^2=r^2 \ \ \ [3]

Subtracting [3] from [2]

-41-2h+12k=0 \ \ \ [4]

Substituting [1] into [4]

-41-2h+12(8/9h+7)=0

43+26/3h=0

h=-129/26

Substituting in [1]

k=8/9(-129/26)+7=101/39

Substituting h and k in [2]

(4+129/26)^2+(1-101/39)^2=r^2=503977/6084

Equation is:

(x+129/26)^2+(y-101/39)^2=503977/6084

GRAPH:

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