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Find an equation of the tangent line to the hyperbola: x^2/a^2  y^2/b^2 = 1 at the point (x0,x1)
 2 years ago
 2 years ago
Find an equation of the tangent line to the hyperbola: x^2/a^2  y^2/b^2 = 1 at the point (x0,x1)
 2 years ago
 2 years ago

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satellite73Best ResponseYou've already chosen the best response.0
implicit diff for this one
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
\[\frac{2x}{a^2}\frac{2y}{b^2}y'=0\] \[y'=\frac{x}{a^2}\times \frac{b^2}{y}=\frac{b^2x}{a^2y}\]
 2 years ago

calyneBest ResponseYou've already chosen the best response.0
yeah i got that but so what's the equation of the tangent line i don't get the textbook's answer
 2 years ago

exravenBest ResponseYou've already chosen the best response.0
\[\frac{2x}{a^{2}}\frac{2y}{b^{2}}y'=0\]\[y'=\frac{b^{2}x}{a^{2}y}\]\[m=\frac{b^{2}x_{0}}{a^{2}x_{1}}\]the equation of the tangent line is\[yx_{1}=\frac{b^{2}x_{0}}{a^{2}x_{1}}\left( xx_{0} \right)\]
 2 years ago

calyneBest ResponseYou've already chosen the best response.0
yeah well the textbook says x0x/a^2  y0y/b^2 = 1 so what's that about
 2 years ago

exravenBest ResponseYou've already chosen the best response.0
algebra..\[yx_{1}=\frac{b^{2}x_{0}}{a^{2}x_{1}}\left( xx_{0} \right)\]\[a^{2}x_{1}ya^{2}x_{1}^{2}=b^{2}x_{0}xb^{2}x_{0}^{2}\]\[b^{2}x_{0}^{2}a^{2}x_{1}^{2}=b^{2}x_{0}xa^{2}x_{1}y\]look back at the hyperbola equation, plug the point (x0,x1)\[\frac{x_{0}^{2}}{a^{2}}\frac{x_{1}^{2}}{b^{2}}=1\]\[b^{2}x_{0}^{2}a^{2}x_{1}^{2}=a^{2}b^{2}\]substitute to the tangent line equation
 2 years ago

exravenBest ResponseYou've already chosen the best response.0
\[a^{2}b^{2}=b^{2}x_{0}xa^{2}x_{1}y\]\[\frac{x_{0}x}{a^{2}}\frac{x_{1}y}{b^{2}}=1\]same as what the textbook said :)
 2 years ago
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