The locus of the point of intersection of two | vedclass

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(C) The locus of the point of intersection of two perpendicular tangents to an ellipse is known as its director circle.The equation of the director ci

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$x^2 + y^2 = 13$

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(C) The locus of the point of intersection of two perpendicular tangents to an ellipse is known as its director circle.The equation of the director circle for an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is given by $x^2 + y^2 = a^2 + b^2$.Given the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,we have $a^2 = 9$ and $b^2 = 4$.Substituting these values into the equation,we get $x^2 + y^2 = 9 + 4$,which simplifies to $x^2 + y^2 = 13$.

The locus of the point of intersection of two perpendicular tangents to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ is:

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