Statement 1 : For the ellipse `(x^2)/5+(y^2)/3=1` , the product of the perpendiculars drawn from the foci on any tangent is 3. Statement 2 : For the ellipse `(x^2)/5+(y^2)/3=1` , the foot of the perpendiculars drawn from the foci on any tangent lies on the circle `x^2+y^2=5` which is an auxiliary circle of the ellipse.

Options

A. 2
B. 3
C. 4
D. 5

Answer

B

Explanation

We know that the product of the perpendiculars from the two foci of an ellipse upon any tangent is equal to the square of the semi-minor axis. Thus
`(S_(1)F_(1))(S_(2)F_(2))=3`