The locus of the point of intersection of perpendicular tangents to the ellipse is called

Hyperbola

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Ellipse

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Auxiliary circle

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Director circle

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Solution

The correct option is D Director circle
It is fundamental fact that : Locus of point of intersection of
perpendicular tangents to the ellipse is called "director circle"

Equation of director circle of ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$
is given by $x^{2} + y^{2} = a^{2} + b^{2}$

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\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

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Find the locus of point of intersection of perpendicular tangents to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

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