JEE MATHEMATICS MCQ: ELLIPSE

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Application +4 | -1

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse

\frac{x^2}{9}+\frac{y^2}{4}=1

from any of its foci

View answer and explanation

Correct option: C

(1,2 \sqrt{2})

Option C (

(1,2 \sqrt{2})

) is correct because the locus of the foot of the perpendicular from the foci to any tangent of the ellipse is the auxiliary circle,

x^2 + y^2 = a^2

, where a=3. Substituting the point

(1,2\sqrt{2})

satisfies the equation

x^2 + y^2 = 9

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O