document.write( "Question 623929: I need help with this circle problem it annoying me at this point can someone explain what i need to do in steps. Also need to identify H,K,R\r
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\n" ); document.write( "\n" ); document.write( "Find the equation of the circle whose diameter has endpoints (-9, -2) and (1, 1). Write it in the form
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Algebra.Com's Answer #392420 by math-vortex(648) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Hi there,\r\n" );
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document.write( "The problem:\r\n" );
document.write( "Find the equation of the circle whose diameter has endpoints (-9, -2) and (1, 1). Write it in the form\r\n" );
document.write( "(x-h)^2 + (y-k)^2 = r^2. Identify the center of the circle (h.k) and its radius r.\r\n" );
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document.write( "A Solution:\r\n" );
document.write( "This problem has a lots parts. I can see why you might be feeling frustrated. We'll take this step \r\n" );
document.write( "by step.\r\n" );
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document.write( "We have two points on the circle that are endpoints of one of its diameters. A diameter always \r\n" );
document.write( "passes through the center of the circle. In fact, the center is the midpoint of the diameter.\r\n" );
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document.write( "We can use the midpoint formula to find the center of the circle. The midpoint formula is\r\n" );
document.write( "M(x,y) = ((x[1]+x[2])/2 , (y[1]+y[2])/2)\r\n" );
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document.write( "The center C of this circle is located at the point (h,k) midway between (x[1],y[1]=(1,1) and \r\n" );
document.write( "(x[2],y[2])=(-9,-2). Using the midpoint formula, we have\r\n" );
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document.write( "C(h,k) = ((-9+1)/2 , (-2+1)/2)\r\n" );
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document.write( "Simplifying, we get,\r\n" );
document.write( "C(h,k) = (-4,-1/2)\r\n" );
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document.write( "The center of the circle is at the point (-4,-1/2). Using the vertex form for the equation for a circle,\r\n" );
document.write( "substitute these values for h and k.\r\n" );
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document.write( "Simplify.\r\n" );
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document.write( "We know that those endpoints to the diameter are actually points on the circle, so we can substitute\r\n" );
document.write( "one of them into the equation for x and y. Then we'll be able to solve for r^2. Either point will work;\r\n" );
document.write( "let's use (1,1).\r\n" );
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document.write( "Simplify and solve for r^2.\r\n" );
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document.write( "We have (h,k) and r^2, so we can write our whole equation.\r\n" );
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document.write( "This is the vertex form of the equation, but the radius is r not r^2. So we take the square root of \r\n" );
document.write( "109/4 to get the radius.\r\n" );
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document.write( "So, the center of your circle is (h,k)=(-4, -1/2) and the radius of the circle is r = (1/2)*sqrt(109)\r\n" );
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document.write( "Please email me if you have questions about any of this. I'd appreciate the feedback and it will help \r\n" );
document.write( "me become a better \"explainer.\"\r\n" );
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document.write( "Ms.Figgy\r\n" );
document.write( "mth.in.the.vortex@gmail.com\r\n" );
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