document.write( "Question 984216: Pls u guys should help me out. The equation of a circle is given as x2 +y2-6x+8y-24=0. Find the equation of the diameter of the circle which passes through the point (-1,1) \n" ); document.write( "

Algebra.Com's Answer #604973 by macston(5194) $\"\"$ $\"About$

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\n" ); document.write( " $\"x%5E2%2By%5E2-6x%2B8y-24=0\"$
\n" ); document.write( " $\"%28x%5E2-6x%29%2B%28y%5E2%2B8y%29=24\"$ Complete the squares
\n" ); document.write( " $\"%28x%5E2-6x%2B9%29%2B%28y%5E2%2B8y%2B16%29=24%2B9%2B16\"$
\n" ); document.write( " $\"%28x-3%29%5E2%2B%28y%2B4%29%5E2=7%5E2\"$
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\n" ); document.write( "Standard form for circle:
\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"$
\n" ); document.write( "Where (h,k) is center of circle and r=radius.
\n" ); document.write( "So the center of our circle is at (3,-4) with radius=7.
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\n" ); document.write( "The equation of the diameter will be the equation through the center and the given point:
\n" ); document.write( "Find the line through (-1,1) and (3,-4)
\n" ); document.write( ".
\n" ); document.write( "Find the slope:
\n" ); document.write( "m=(change in y)/(change in x)=(1-(-4))/(-1-3)=(5/-4)=-(5/4)
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\n" ); document.write( "In slope intercept form:
\n" ); document.write( "y=mx+b
\n" ); document.write( "y=-(5/4)x+b Put in values of the given point and solve for b.
\n" ); document.write( "1=-(5/4)(-1)+b
\n" ); document.write( "4/4=5/4+b
\n" ); document.write( "-1/4=b
\n" ); document.write( ".
\n" ); document.write( "Write the final equation:
\n" ); document.write( "y=-(5/4)x-1/4\r
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