document.write( "Question 1014225: Find the equation of the circle in general form, tangent to 5-y=3 at (2,7) and its center is on the line x+2y=19 \n" ); document.write( "
Algebra.Com's Answer #630583 by Cromlix(4381)\"\" \"About 
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Hi there,
\n" ); document.write( "I am assuming that you have missed out
\n" ); document.write( "an x in your equation.
\n" ); document.write( "5 - y = 3
\n" ); document.write( "should read
\n" ); document.write( "5x - y = 3
\n" ); document.write( "Putting in the form y = mx + c
\n" ); document.write( "y = 5x - 3
\n" ); document.write( "Finding the gradient of the line
\n" ); document.write( "at right angles from y = 5x - 3
\n" ); document.write( "Lines at right angles have gradients
\n" ); document.write( "that multiply together to give -1
\n" ); document.write( "m1 x m2 = -1
\n" ); document.write( "So, line at right angles has gradient
\n" ); document.write( "of -1/5
\n" ); document.write( "Using the points (2,7) in the line
\n" ); document.write( "equation y - b = m(x - a)
\n" ); document.write( "y - 7 = -1/5(x - 2)
\n" ); document.write( "y = -1/5x + 2/5 + 35/5 (7)
\n" ); document.write( "y = -1/5x + 37/5
\n" ); document.write( "Multiply thro' by 5
\n" ); document.write( "5y = -x + 37
\n" ); document.write( "5y + x = 37....Equation (1)
\n" ); document.write( "Using the equation x + 2y = 19
\n" ); document.write( "Rearranging gives 2y + x = 19 .....Equation (2)
\n" ); document.write( "Solving simultaneous equations.
\n" ); document.write( "5y + x = 37....Equation (1)
\n" ); document.write( "2y + x = 19 ...Equation (2)
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "3y = 18
\n" ); document.write( "y = 6
\n" ); document.write( "Substitute y = 6 into Equation (1)
\n" ); document.write( "5y + x = 37
\n" ); document.write( "5(6) + x = 37
\n" ); document.write( "30 + x = 37
\n" ); document.write( "x = 37 - 30
\n" ); document.write( "x = 7
\n" ); document.write( "Centre of the circle = {7,6}
\n" ); document.write( "Distance from (7,6) to (2,7)
\n" ); document.write( "√(x2 - x1)^2 + (y2 - y1)^2
\n" ); document.write( "√(2 - 7)^2 + (7 - 6)^2
\n" ); document.write( "√(-5)^2 + (1)^2
\n" ); document.write( "√ 25 + 1
\n" ); document.write( "√26
\n" ); document.write( "This is the radius.
\n" ); document.write( "General form of circle
\n" ); document.write( "(x - a)^2 + (y - b)^2 = r^2
\n" ); document.write( "(x - 7)^2 + (y - 6)^2 = 26
\n" ); document.write( "Hope this helps :-) \n" ); document.write( "
\n" );