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Korolek [52]
3 years ago
6

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

Mathematics
1 answer:
musickatia [10]3 years ago
8 0

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

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

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