The centre of the circle passing through the points (8,12),(11,3) and (0,14) is​

Let the equation of the circle be x2+y2+2gx+2fy+c=0 (i)

Then its centre will be O=(−g,−f). 

It passes through A=(x1,y1)=(8,12),B=(x2,y2)=(11,3) and C=(x3,y3)=(0,14). 

Substituting (x,y)=(x1,y1)=(8,12),(x2,y2)=(11,3) and (x3,y3)=(0,14) in equation (i) and simplifying, we get 

16g+24y+c=−208 (ii),

22g+6f+c=−130 (iii)

and 28f+c=−196 (iv) 

Eliminating c from (ii) and (iii),

g=3f+13 (v)

Again eliminating c from (iii) and (iv), we have

g=f+3 (vi)

∴ From (v) and (vi), we get

3f+13=f+3

Putting f=−5 in (vi),  have

g=−2

∴ Centre O=(−g,−f)=(2,5)

(2,5)

#CarryOnLearning

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you