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WB JEE 2009

MCQ (Single Correct Answer)

The total number of tangents through the point (3, 5) that can be drawn to the ellipse 3x2 + 5y2 = 32 and 25x2 + 9y2 = 450 is

A
0
B
2
C
3
D
4

Explanation

$$\because$$ 3 . 32 + 5 . 52 $$-$$ 32 > 0

$$\therefore$$ From (3, 5) we can draw 2 tangents to the ellipse

3x2 + 5y2 = 32. Again 25 . 32 + 9 . 52 $$-$$ 450 = 0

$$\therefore$$ From (3, 5) we can draw only 1 tangent to the ellipse

25x2 + 9y2 = 450 $$\therefore$$ Required number of tangents = 2 + 1 = 3

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