document.write( "Question 200956: A manufacturer of cartridges for stereo systems has designed a stylus with parabolic cross section. The equation of the parabola is y=16x^2 where x and y are measured is millimeters . If the stylus sits in a record groove whose sides make an angle with the horizontal direction where tan of the angle = 1.75 , find the points of contact P and Q of the stylus with the groove. \n" ); document.write( "

Algebra.Com's Answer #151220 by josmiceli(19441) $\"\"$ $\"About$

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Have you had calculus? That's the
\n" ); document.write( "easiest way to do it. If the equation
\n" ); document.write( "is $\"y+=+16x%5E2\"$ , then the equation
\n" ); document.write( "of the slope at every point is
\n" ); document.write( " $\"y%27+=+32x\"$ .
\n" ); document.write( "If I say $\"32x+=+1.75\"$ and
\n" ); document.write( " $\"32x+=+-1.75\"$ , These are the x-
\n" ); document.write( "values of the points of contact
\n" ); document.write( " $\"32x+=+1.75\"$
\n" ); document.write( " $\"x+=+.0546875\"$
\n" ); document.write( "and
\n" ); document.write( " $\"32x+=+-1.75\"$
\n" ); document.write( " $\"x+=+-.0546875\"$
\n" ); document.write( "And the y-coordinates are:
\n" ); document.write( " $\"y+=+16x%5E2\"$
\n" ); document.write( " $\"y+=+16%2A%28.0546875%29%5E2\"$
\n" ); document.write( " $\"y+=+16%2A2.9907226\"$
\n" ); document.write( " $\"y+=+.0478515\"$
\n" ); document.write( "The y-coodinate for the other value is
\n" ); document.write( "the same, since parabola is symmetric
\n" ); document.write( "about y-axis
\n" ); document.write( "P(-.05469, .04785) and
\n" ); document.write( "Q(.05469, .04785) are the points of contact in mm \n" ); document.write( "

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