document.write( "Question 972005: Find the equation of r = 1/(2 + sinθ) in rectangular form.Show the step-by-step process. \n" ); document.write( "
Algebra.Com's Answer #594411 by stanbon(75887)![]() ![]() ![]() You can put this solution on YOUR website! Find the equation of r = 1/(2 + sinθ) in rectangular form.Show the step-by-step process. \n" ); document.write( "----- \n" ); document.write( "Conversion forms: \n" ); document.write( "r = sqrt(x^2+y^2) \n" ); document.write( "theta = arctan(y/x) \n" ); document.write( "----------------------------- \n" ); document.write( "Your problem:: \n" ); document.write( "sqrt(x^2+y^2) = 1/(2 + (y/sqrt(x^2+y^2)) \n" ); document.write( "------ \n" ); document.write( "Cross-multiply to get: \n" ); document.write( "2sqrt(x^2+y^2) + y = 1 \n" ); document.write( "------- \n" ); document.write( "2sqrt(x^2+y^2) = 1-y \n" ); document.write( "Square both sides to get: \n" ); document.write( "4(x^2+y^2) = 1 - 2y + y^2 \n" ); document.write( "------- \n" ); document.write( "4x^2 + 4y^2 = 1 - 2y + y^2 \n" ); document.write( "------ \n" ); document.write( "1-2y = 4x^2 + 3y^2 \n" ); document.write( "------- \n" ); document.write( "3y^2 + 2y + 4x^2 = 1 \n" ); document.write( "Complete the square to get: \n" ); document.write( "------- \n" ); document.write( "3(y^2+(2/3)y + (1/9) + 4x^2 = 1+ 3(1/9) \n" ); document.write( "---- \n" ); document.write( "3(y+(1/3))^2 + 4x^2 = (4/3) \n" ); document.write( "------ \n" ); document.write( "(y+(1/3))^2/(4/9) + 4x^2/(4/3) = 1 \n" ); document.write( "---------------------------------------- \n" ); document.write( "Cheers, \n" ); document.write( "Stan H. \n" ); document.write( "---------------\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |