document.write( "Question 659135: Find the equation of asymptotes of the hyperbola 9y^2-4x^2=36 and obtain the product of the perpendicular distances between any point of the hyperbola and the asymptotes? \n" ); document.write( "
Algebra.Com's Answer #411373 by lwsshak3(11628)\"\" \"About 
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Find the equation of asymptotes of the hyperbola 9y^2-4x^2=36 and obtain the product of the perpendicular distances between any point of the hyperbola and the asymptotes?
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\n" ); document.write( "\n" ); document.write( "9y^2-4x^2=36
\n" ); document.write( "y^2/4-x^2/9=1
\n" ); document.write( "This is an equation of a hyperbola with vertical transverse axis
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\n" ); document.write( "a^2=4
\n" ); document.write( "a=2
\n" ); document.write( "b^2=9
\n" ); document.write( "b=3
\n" ); document.write( "slopes of asymptotes: ±a/b=±2/3
\n" ); document.write( "equations of asymptotes: y=2x/3 and y=-2x/3
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\n" ); document.write( "The line representing the perpendicular distance between any point of the hyperbola and the asymptotes has a slope=negative reciprocal of the asymptotes=±3/2. Since slope=∆y/∆x, the distance formula can be used to determine the perpendicular distance. I'm not sure what is meant by \"product of perpendicular distances\".\r
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