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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 |
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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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