Tangent to the ellipse ` (x^(2))/(32)+(y^(2))/(18)=1` having slope `-(3)/(4)` meet the coordinates axes in A and B. Find the area of the `DeltaAOB` , where O is the origin .

Tangent at a point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is drawn which cuts the coordinates axes at A and B the maximum area of the triangle OAB is ( O being origin )

Tangent at a point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is drawn which cuts the coordinates axes at A and B the minimum area of the triangle OAB is ( O being origin )

If the tangent at a point on the ellipse (x^(2))/(27)+(y^(2))/(3)=1 meets the coordinate axes at A and B, and the origin,then the minimum area (in sq.units) of the triangle OAB is:

A tangent having slope (-4)/(3) to the ellipse (x^(2))/(18)+(y^(2))/(32)=1 intersects the major and minor axes at A and B .If o is origin,then the area of , Delta OAB is k sq.units where sum of digits of k is

If the tangent at any point on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 intersects the coordinate axes at P and Q , then the minimum value of the area (in square unit ) of the triangle OPQ is (O being the origin )-

If the tangent drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at any point P meets the coordinate axes at the points A and B respectively. If the rectangle OACB (O being the origin) is completed, where C lies on (x^2)/(a^2)-(y^2)/(b^2)=lambda . Then, the value of lambda is: