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  • On which curve does the perpendicular tangents drawn to the hyperbola <img alt="\mathrm{25 x^2-81 y^2=2025}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B25%20x%5E2-81%20y%5E2%3

On which curve does the perpendicular tangents drawn to the hyperbola \mathrm{25 x^2-81 y^2=2025} intersect?

Option: 1

\mathrm{x^2+y^2=56}


Option: 2

\mathrm{x^2-y^2=65}


Option: 3

\mathrm{x^2+y^2=65}


Option: 4

\mathrm{\text { None of these }}


Answers (1)

best_answer

The locus of the point of intersection of perpendicular

tangents to\mathrm{ \frac{x^2}{81}-\frac{y^2}{25}=1} is the director circle given by

\mathrm{x^2+y^2=a^2-b^2}
Hence, the perpendicular tangents drawn to \mathrm{\frac{x^2}{81}-\frac{y^2}{25}=1}Intersect on the curve

\mathrm{ x^2+y^2=81-25=81-25=56 }

Posted by

Ajit Kumar Dubey

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