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Find the magnitude of the slope of the tangent drawn at an extremity of a latus rectum of the hyperbola x²/a² - y²/b² = 1, where e is the eccentricity of the hyperbola.
- e
- b*e
- a*b
- a*e
Correct answer: e
Solution
Differentiating gives dy/dx = b² x/(a² y); at (ae, b²/a) this becomes b²(ae)/(a² * b²/a) = e, so the slope magnitude is e.
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