document.write( "Question 83412: A circle contains the points (0,0), (-7,-17), and (18,-12). Solve a system of three equations in h,k, and r and give the equation of the circle. Show work. (The teacher gave the hint: Use given (x,y) pairs in \"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\" to get 3 equations to solve the system using substition or elimination. I tried to do this, but got stuck...can you do both substitution and elimination in the same problem?) \n" ); document.write( "
Algebra.Com's Answer #60033 by ankor@dixie-net.com(22740)\"\" \"About 
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A circle contains the points (0,0), (-7,-17), and (18,-12). Solve a system of three equations in h,k, and r and give the equation of the circle. Show work. (The teacher gave the hint: Use given (x,y) pairs in (x-h)^2+(y-k)^2 = r^2 to get 3 equations to solve the system using substitution or elimination.
\n" ); document.write( ":
\n" ); document.write( "Eq1 (0,0):
\n" ); document.write( "(0-h)^2 + (0-k) = r^2
\n" ); document.write( "h^2 + k^2 = r^2
\n" ); document.write( ":
\n" ); document.write( "Eq2 (-7,-17):
\n" ); document.write( "(-7-h)^2 + (-17-k)^2 = r^2
\n" ); document.write( "(49 + 14h + h^2) + (289 + 34k + k^2) = r^2
\n" ); document.write( "h^2 + 14h + k^2 + 34k + 338 = r^2
\n" ); document.write( ":
\n" ); document.write( "Eq3 (18,-12)
\n" ); document.write( "(18-h)^2 + (-12-k)^2 = r^2
\n" ); document.write( "324 - 36h + h^2 + 144 + 24k + k^ = r^2
\n" ); document.write( "h^2 - 36h + k^2 + 24k + 468 = r^2
\n" ); document.write( ":
\n" ); document.write( "If you subtract eq 1 from eq 2 you get:
\n" ); document.write( "14h + 34k + 338 = 0
\n" ); document.write( "or
\n" ); document.write( "14h + 34k = -338
\n" ); document.write( ":
\n" ); document.write( "If you subtract eq 1 from eq 3 you get:
\n" ); document.write( "-36h + 24k + 468 = 0
\n" ); document.write( "or
\n" ); document.write( "-36h + 24k = -468
\n" ); document.write( ":
\n" ); document.write( "Two equations, two unknowns
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\n" ); document.write( "Multiply the 1st eq by 36 and the 2nd eq by 14 to eliminate h, find k:
\n" ); document.write( " 504h + 1224k = -12168
\n" ); document.write( "-504h + 336k = - 6552
\n" ); document.write( "--------------------------adding eliminates h
\n" ); document.write( " 0h + 1560k = -18720
\n" ); document.write( "k = -18720/1560
\n" ); document.write( "k = -12
\n" ); document.write( ":
\n" ); document.write( "Find h using: 14h + 34k = -338; substitute -12 for k
\n" ); document.write( "14h + 34(-12) = -338
\n" ); document.write( "14h - 408 = - 338
\n" ); document.write( "14h = -338 + 408
\n" ); document.write( "14h = +70
\n" ); document.write( "h = 70/14
\n" ); document.write( "h = +5
\n" ); document.write( ":
\n" ); document.write( "We have h = +5 and k = -12; use h^2 + k^2 = r^2 to find r
\n" ); document.write( ":
\n" ); document.write( "25 + 144 = r^2
\n" ); document.write( "169 = r^
\n" ); document.write( "r = sqrt(169)
\n" ); document.write( "r = 13
\n" ); document.write( ":
\n" ); document.write( "Did this help? \n" ); document.write( "
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