The minimum area of the triangle formed by the tangent to `(x^2)/(a^2)+(y^2)/(b^2)=1` and the coordinate axes is (a)`a b` sq. units (b) `(a^2+b^2)/2s qdot""u n i t s` (c)`((a+b)^2)/2s qdot""u n i t s` (d) `(a^2+a b+b^2)/3` sq. units

The area of the triangle formed by the positive x- axis and the normal and tangent to the circle x^2+y^2=4 at (1,sqrt(3)) is (a) 2sqrt(3)s qdotu n i t s (b) 3sqrt(2)s qdotu n i t s (c) sqrt(6)s qdotu n i t s (d) none of these

Area bounded by the curve x y^2=a^2(a-x) and the y-axis is (pia^2)/2s qdotu n i t s (b) pia^2s qdotu n i t s (c) 3pia^2s qdotu n i t s (d) None of these

If the extremities of the base of an isosceles triangle are the points (2a ,0) and (0, a), and the equation of one of the side is x=2a , then the area of the triangle is (a) 5a^2s qdotu n i t s (b) (5a^2)/2s qdotu n i t s (c) (25 a^2)/2s qdotu n i t s (d) none of these

Area of the triangle formed by the line x+y=3 and the angle bisectors of the pairs of straight lines x^2-y^2+2y=1 is (a) 2sq units (b) 4sq units (c) 6sq units (d) 8sq units

The area of the quadrilateral formed by the tangents at the endpoint of the latus rectum to the ellipse (x^2)/9+(y^2)/5=1 is (A) 27/4 sq. unit (B) 9 sq. units (C) 27/2 sq. unit (D) 27 sq. unit

The area bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is 2/e s qdotu n i t s (b) 1-2/e s qdotu n i t s 1/e s qdotu n i t s (d) 1-1/e s qdotu n i t s

The area of the closed figure bounded by y=(x^2)/2-2x+2 and the tangents to it at (1,1/2) and (4,2) is (A) 9/8 sq.unit (B) 3/8 sq.units (C) 3/2 sq.units (D) 9/4 sq.units

If c^(2) = a^(2) + b^(2) , then prove that 4s (s - a) (s - b) (s - c) = a^(2) b^(2)

A straight line passing through P(3,1) meets the coordinate axes at Aa n dB . It is given that the distance of this straight line from the origin O is maximum. The area of triangle O A B is equal to (50)/3s qdotu n i t s (b) (25)/3s qdotu n i t s (20)/3s qdotu n i t s (d) (100)/3s qdotu n i t s