1.

For 0 lt theta lt (pi)/(2), four tangents are drawn at the four points ( pm 3 cos theta, pm 2 sin theta ) to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 . If A(theta) denote the area of the quadrilateral formed by these four tangents, the minimum value of A(theta) is

Answer»

21
24
27
30

Solution :`{:((X cos theta)/(3)+(y sin theta)/(2)=1),((x cos theta)/(3)-(y sin theta)/(2)=1):}}x= 3 sec theta,y=0`
`(-x cos theta)/(3)+(y sin theta)/(2)=1`
`(-x cos theta)/(3)-(y sin theta)/(2)=1`
`x=0,y=2 cos theta`
AREA `=4.(1)/(2) 3 sin theta. 2 cos theta`
`=(12)/( sin theta cos theta)=(24)/( sin 2 theta)`
`:. ` MIN. area =24


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