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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) is |
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Answer» 21 `(-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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