The number of real tangents that can be drawn to the ellipse 3x²+5y²=32 passing through (3, 5) is,

(A) 0
(B) 1
(C) 2
(D) None of these

Solution

Let us find out if the point (3, 5) lies on the ellipse, outside the ellipse or inside the ellipse.

The value of the expression 3x²+5y²-32 at (3, 5) is > 0.

Hence, the point (3, 5) lies outside the ellipse.

So, two real tangents can be drawn from (3, 5).

Hence, (C)