document.write( "Question 200662: Hi everyone, I was wondering if someone could show me how to find the equation of a circle which has a centrepoint of (-2, 5) and passes through point (1,3). I also need to know what the radius of the circle is.
\n" ); document.write( "If someone could show me how to do the previous with full working, with steps and notation i would be really grateful.
\n" ); document.write( "Thnaks again, -Nick. \n" ); document.write( "

Algebra.Com's Answer #150917 by Alan3354(69443) $\"\"$ $\"About$

You can put this solution on YOUR website!
find the equation of a circle which has a centrepoint of (-2, 5) and passes through point (1,3). I also need to know what the radius of the circle is.
\n" ); document.write( "----------------
\n" ); document.write( "The radius is the distance from the center to the point (1,3), so find that.
\n" ); document.write( "r^2 = diffy^2 + diffx^2
\n" ); document.write( "r^2 = (5-3)^2 + (-2-1)^2 = 4 + 9
\n" ); document.write( "r = sqrt(13)
\n" ); document.write( "-------------
\n" ); document.write( "The center is offset from the Origin by x = 2 and y = -5
\n" ); document.write( "The eqn has the form (x-a)^2 + (y-b)^2 = r^2 where (a,b) is (-2,5)
\n" ); document.write( "So it's
\n" ); document.write( "(x + 2)^2 + (y-5)^2 = 13
\n" ); document.write( "Note that the values are subtracted.
\n" ); document.write( "-----------------
\n" ); document.write( "That can be expanded
\n" ); document.write( "x^2 + 4x + 4 + y^2 - 10y + 25 = 13
\n" ); document.write( "x^2 + 4x + y^2 - 10y = -16
\n" ); document.write( " \n" ); document.write( "

\n" );