thahalbor2shekhat9er
thahalbor2shekhat9er thahalbor2shekhat9er
  • 21-07-2016
  • Mathematics
contestada

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

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meerkat18
meerkat18 meerkat18
  • 22-07-2016

The standard form of a hyperbola is x2/a2 − y2/ b2 = 1
the tangent line is the first derivative of the function
y′ = b^2x/ a^2 y
hence the slope is 
m = b^2 x0 / a^2 x1

Therefore the equation of the tangent line isy−x1 = b^2 x0 / a^2 x1* (x−x0)

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