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)` isA. 21B. 24C. 27D. 30

Answer» Correct Answer - B
`{:((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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