anonymous
  • anonymous
The line 3x-4y=12 is tangent to the parabola y^2=4px find p
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@SolomonZelman
SolomonZelman
  • SolomonZelman
3x-4y=12 ---> -4y=-3x+12 ---> y = (3/4)x - 3
SolomonZelman
  • SolomonZelman
So the slope of your parabola at the point of tangency is 3/4.

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anonymous
  • anonymous
ok
SolomonZelman
  • SolomonZelman
y^2 = 4px y = ±\(\sqrt{4px}\) y = ±2\(\sqrt{px}\) y\('\) = ±p\(/\sqrt{px}\) Where is the slope 3/4? 3/4 = ±p\(/\sqrt{px}\) and it is above the x axis because the slope is positive, so in ± we take the +. 3/4 = p\(/\sqrt{px}\) 3/(4p) = \(1/\sqrt{px}\) (4p)/3 = \(\sqrt{px}\) 4p = 3√(px) -----> first equation
SolomonZelman
  • SolomonZelman
4p = 3√(px) 4p = 3•√p•√x 4√p = 3√x 16p = 9x 16p / 9 = x ---> point of tangency
SolomonZelman
  • SolomonZelman
oh sorry we choose the below the x-axis part. SO http://www.wolframalpha.com/input/?i=%283%2F4%29%2816p+%2F+9%29+-+3+%3D+-2%E2%88%9A%28p%2816p+%2F+9%29%29
anonymous
  • anonymous
so what do we do with the point of tangency
SolomonZelman
  • SolomonZelman
https://www.desmos.com/calculator/bj3xaweyae
SolomonZelman
  • SolomonZelman
I solved for p via wolfram and there we see it is once tangent to the p=-9/4 version parabola.

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