Question:
Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse,
$\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$ from any of its foci?
Correct Option: 3,
Solution:
We know that the locus of the feet of the perpendicular
draw from foci to any tangent of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ is
the auxiliary circle $x^{2}+y^{2}=a^{2}$
$\therefore$ Auxiliary circle $: x^{2}+y^{2}=4$
$\therefore$ Auxiliary circle $: x^{2}+y^{2}=4$
$\therefore(-1, \sqrt{3})$ satisfies the given equation.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.