ellipse

the no. of values of Î¸ Îµ[0,2Ï€] for which the line 2xcosÎ¸+3ysinÎ¸=6 touches the ellipse 4x²+9y² =36 is
(a)4 (b)2 (c)1 (d)âˆž

4 Answers

1357

Manish Shankar ·2008-11-23 08:55:17

infinite..

because.. this is the general equation of the tangent :)

think in terms of general ellipse and a general tangent at any pont

(a cos theta, b sin theta )

ans-4

1357

Manish Shankar ·2008-11-23 09:41:10

in the interval these straight 5 points 0,Ï€/2,Ï€,3Ï€/2,2Ï€ satisfy the required condition
how can it be less than 5 ?

Diiferentiate eqn of ellipse, get dy/dx and equate with slope of the line
On differentiation,
8x+18y.y'=0
y'=-4x/9y

slope of line is -2cosÎ¸/3sinÎ¸(=-2cotÎ¸/3)
-2cotÎ¸/3=-4x/9y
cotÎ¸=2x/3y=> Î¸=cot^-1(2x/3y)
=> Infinite values

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