SOLUTION: 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 millimete

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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.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Have you had calculus? That's the
easiest way to do it. If the equation
is y+=+16x%5E2 , then the equation
of the slope at every point is
y%27+=+32x.
If I say 32x+=+1.75 and
32x+=+-1.75, These are the x-
values of the points of contact
32x+=+1.75
x+=+.0546875
and
32x+=+-1.75
x+=+-.0546875
And the y-coordinates are:
y+=+16x%5E2
y+=+16%2A%28.0546875%29%5E2
y+=+16%2A2.9907226
y+=+.0478515
The y-coodinate for the other value is
the same, since parabola is symmetric
about y-axis
P(-.05469, .04785) and
Q(.05469, .04785) are the points of contact in mm