anonymous
  • anonymous
Find the equation of the tangent to the following parabola a) y^2=12x ; the tangent having slope -1/3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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SolomonZelman
  • SolomonZelman
The first thing you need to know is - where does the parabola have a slope -1/3, so that the tangent line would have the slope -1/3 ?
SolomonZelman
  • SolomonZelman
\(y=\pm\sqrt{12x}\) \(y'=\pm\dfrac{6}{\sqrt{12x}}\) \(\dfrac{-1}{3}=\pm\dfrac{6}{\sqrt{12x}}\)
SolomonZelman
  • SolomonZelman
we would need to take the bottom half of the parabola.

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anonymous
  • anonymous
where did u get that 6 frm \[\frac{ 6 }{ \sqrt{12x} }\]
SolomonZelman
  • SolomonZelman
-1 / 3 = -6 / √(12x) 1 / 3 = 6 / √(12x) √(12x) = 18 12x = 324 x = 324/12 = 27
SolomonZelman
  • SolomonZelman
y' = 1/ ( 2 √(12x)) * 12 = 6/ √(12)
SolomonZelman
  • SolomonZelman
and ± comes from taking the square root on both sides
anonymous
  • anonymous
ok
SolomonZelman
  • SolomonZelman
so I get that it is going through y = -(1/3) - 9 https://www.desmos.com/calculator/vpujilagiw
anonymous
  • anonymous
so thats the equation?
SolomonZelman
  • SolomonZelman
I forgot the x by the slope, oopsis
SolomonZelman
  • SolomonZelman
-(1/3)x - 9

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