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  • Through the positive vertex of the hyperbola <img alt="\mathrm{\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfrac%7Bx%5E%7B2%7D%7D

Through the positive vertex of the hyperbola \mathrm{\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1}  a tangent is drawn, where does it meet the conjugate hyperbola

Option: 1

at the points ( \pm \mathrm{a} \sqrt{2}, \mathrm{~b})


Option: 2

at the points (0,0)


Option: 3

at the points ( \pm \mathrm{a}, \mathrm{b})


Option: 4

at the points (\mathrm{a}, \pm \mathrm{b} \sqrt{2})


Answers (1)

best_answer

Equation of tangent is \mathrm{x}=\mathrm{a}, solving it with \frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=-1.

We get the points as (a, \pm b \sqrt{2}).

Posted by

HARSH KANKARIA

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