If the plane `x/2+y/3+z/6=1` cuts the axes of coordinates at points, `A ,B ,a n dC` , then find the area of the triangle `A B Cdot` a. `18s qdot` unit b. `36s qdot` unit c. `3sqrt(14)s qdot` unit d. `2sqrt(14)s qdot` unit

Area of the triangle formed by the line x+y=3 and angle bisectors of the pair of straight lines x^2-y^2+2y=1 is a. 2s qdotu n i t s b. 4s qdotu n i t s c. 6s qdotu n i t s d. 8s qdotu n i t s

The area bounded by the loop of the curve 4y^2=x^2(4-x^2) is (a)7/3 sq. units (b) 8/3s qdotu n i t e s (c)(11)/3s qdotu n i t s (d) (16)/3s qdotu n i t s

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O P.O Q=p^2 , then find the locus of the point Qdot

Consider two curves C_1: y^2=4[sqrt(y)]x a n dC_2: x^2=4[sqrt(x)]y , where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines x=1,y=1,x=4,y=4 is (a) 8/3s qdotu n i t s (b) (10)/3s qdotu n i t s (c) (11)/3s qdotu n i t s (d) (11)/4s qdotu n i t s

The straight lines 7x-2y+10=0 and 7x+2y-10=0 form an isosceles triangle with the line y=2. The area of this triangle is equal to(a) (15)/7s qdotu n i t s (b) (10)/7s qdotu n i t s (c)(18)/7s qdotu n i t s (d) none of these

If the angles of a triangle are 30^0a n d45^0 and the included side is (sqrt(3)+1) cm, then area of the triangle is 1/2(sqrt(3)+1)sq units area of the triangle is 1/2(sqrt(3)-1)sq units

A variable plane passes through a fixed point (a ,b ,c) and cuts the coordinate axes at points A ,B ,a n dCdot Show that locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.

The area of the closed figure bounded by x=-1,x=2,a n d y={-x^2+2,xlt=1 2x-1,x >1 and the ascissa axis is (a) (16)/3s qdotu n i t s (b) (10)/3s qdotu n i t s (c) (13)/3s qdotu n i t s (d) 7/3s qdotu n i t s

The area inside the parabola 5x^2-y=0 but outside the parabola 2x^2-y+9=0 is (a) 12sqrt(3) sq units (b) 6sqrt(3) sq units (c) 8sqrt(3) sq units (d) 4sqrt(3) sq units

Let the plane (x)/(a)+(y)/(b)+(z)/(c)=1 cut the axes at A, B, C respectively .Prove that the area of the triangle ABC is given by (1)/(2)sqrt(b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2)) .