SOLUTION: Find the equation of the circle that passes through (-1,1) and with centre at the point of intersection of x + 3y + 7 = 0 and 3x - 2y - 12 = 0.

Algebra ->  Circles -> SOLUTION: Find the equation of the circle that passes through (-1,1) and with centre at the point of intersection of x + 3y + 7 = 0 and 3x - 2y - 12 = 0.      Log On


   



Question 1078546: Find the equation of the circle that passes through (-1,1) and with centre at the point of intersection of x + 3y + 7 = 0 and 3x - 2y - 12 = 0.
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the point of intersection.
x=-3y-7
Substitute into the second equation,
3%28-3y-7%29-2y-12=0
-9y-21-2y-12=0
-11y-33=0
-11y=33
y=-3
So,
x=-3%28-3%29-7
x=9-7
x=2
So then,
%28x-2%29%5E2%2B%28y-%28-3%29%29%5E2=R%5E2
%28x-2%29%5E2%2B%28y%2B3%29%5E2=R%5E2
Using the point,
%28-1-2%29%5E2%2B%281%2B3%29%5E2=R%5E2
%28-3%29%5E2%2B4%5E2=R%5E2
R%5E2=9%2B16
R%5E2=25
Finally,
%28x-2%29%5E2%2B%28y%2B3%29%5E2=25

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the equation of the circle that passes through (-1,1) and with center at the point of intersection of x+%2B+3y+%2B+7+=+0 and 3x+-+2y+-+12+=+0.

equation of the circle:
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2+where+%7B%7B%7Bh and k are x and y coordinates of center, and r is radius
use x+%2B+3y+%2B+7+=+0 and 3x+-+2y+-+12+=+0 to find x and y coordinates of center
x+%2B+3y+%2B+7+=+0...........solve for x
x+=-3y-7............substitute in equation
3%28-3y-7%29+-+2y+-+12+=+0
-9y+-21-+2y+-+12+=+0
-11y+-33+=+0
-11y+=+33
y+=+33%2F-11
y+=+-3
find x%7D%7D%0D%0A%0D%0A%7B%7B%7Bx+=-3%28-3%29-7
x+=9-7
x+=2
so, x=h and y=k coordinates of center are: 2 and -3
and equation of your circle (so far) is:

use given point (-1,1) and substitute its x and y coordinates
%28-1-2%29%5E2%2B%281%2B3%29%5E2=r%5E2
%28-3%29%5E2%2B%284%29%5E2=r%5E2
9%2B16=r%5E2
25=r%5E2
%28x-2%29%5E2%2B%28y%2B3%29%5E2=25+ ->equation of your circle