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  • The number of possible tangents which can be drawn to the curve ,

The number of possible tangents which can be drawn to the curve \mathrm{4 x^2-9 y^2=36}, which are perpendicular to the straight line \mathrm{5 x+2 y-10=0}, is

Option: 1

- 1


Option: 2

2


Option: 3

4


Option: 4

0


Answers (1)

best_answer

Tangent to \mathrm{\frac{x^2}{9}-\frac{y^2}{4}=1 ~at ~P(3 \sec \theta, 2 \tan \theta)} is

\mathrm{\frac{x}{3} \sec \theta-\frac{y}{2} \tan \theta=1 }
This is perpendicular to \mathrm{5 x+2 y-10=0}

\mathrm{\therefore \frac{2 \sec \theta}{3 \tan \theta}=\frac{2}{5} \text { or } \sin \theta=\frac{5}{3} \text {. }}

which is not possible.
Hence, there is no such tangent.

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