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

x^{2} + y^{2} = 4

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x^{2} + y^{2} = 9

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x^{2} + y^{2} = 5

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x^{2} + y^{2} = 13

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Solution

The correct option is D $x^{2} + y^{2} = 13$
The locus of points of intersection of perpendicular tangents to an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is given by the director circle, i.e. $x^{2} + y^{2} = a^{2} + b^{2}$
So here the locus is $x^{2} + y^{2} = 9 + 4 = 13.$

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The locus of the point of intersection of the perpendicular tangents to ellipse x29+y24=1 is

The correct option is D x2+y2=13The locus of points of intersection of perpendicular tangents to an ellipse x2a2+y2b2=1 is given by the director circle, i.e. x2+y2=a2+b2So here the locus is x2+y2=9+4=13.

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

The correct option is D $x^{2} + y^{2} = 13$
The locus of points of intersection of perpendicular tangents to an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is given by the director circle, i.e. $x^{2} + y^{2} = a^{2} + b^{2}$
So here the locus is $x^{2} + y^{2} = 9 + 4 = 13.$