Number of points from where perpendicular tangents can be drawn to the curve $\frac{x^{2}}{16} - \frac{y^{2}}{25} = 1$ is

1

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2

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0

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infinite

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Solution

The correct option is C $0$
If Tangents on the Ellipse are Perpendicular to each other then they must meet at the Director circle

Now, Equation of Director Circle $\to x^{2} + y^{2} = a^{2} - b^{2}$

where Radius of Director Circle $= r = \sqrt{a^{2} - b^{2}}$

But $a^{2} - b^{2} = 16 - 25 = - 9$

hence, Director Circle cannot be possible so there exist no point from which perpendicular tangents can be drawn on the ellipse.

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Number of points from where perpendicular tangents to the curve $\frac{x^{2}}{16} - \frac{y^{2}}{25} = 1$ can be drawn, is:

\frac{x^{2}}{16} + \frac{y^{2}}{25} = 1

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