Permutations an...

If  $$A =  (-3,4) , B =(-1,-2) , C=(5,6) D= (x,-4) $$  are the vertices of a quadrilateral such that area triangle $$ABD= 2 \times$$ (area of a triangle $$ACD$$), then $$x =$$

$$\dfrac { 7 } { 11 } : \dfrac { 336 } { 110 } : ? \quad : \quad \dfrac { 720 } { 272 }$$

A line L passes through the points $$ (1,1)  $$and $$ (2,0)  $$ and another line $$  L^{\prime}  $$ passes through $$ \left(\frac{1}{2}, 0\right)  $$ and perpendicular to L.Then the area of the triangle formed by the lines $$  L, L^{\prime}  $$ and $$  y- $$ axis, is

The area of the triangle formed by the lines $$x=0;y=0$$ and $$x\sin { { 18 }^{ 0 } } +y\cos { { 36 }^{ 0 } } +1=0$$ is 

If $$P , Q$$ are two points on the line $$3 x + 4 y + 15 = 0$$ such that $$O P = O Q = 9$$ then the area of $$\Delta O P Q$$ is

$${\log _5}2,\,\,{\log _6}\,2,\,\,{\log _{12}}\,\,2\,\,$$ are in 

Area of a triangle whose vertices are $$(a\cos \theta ,b\sin \theta ),(-a\sin \theta ,b\cos \theta)$$ and $$(-a\cos \theta ,-b\sin \theta )$$ is-

Area of the triangle formed by the tangents at the points $$\left( {4,6} \right),\left( {10,8} \right)$$ and $$\left( {2,4} \right)$$ on the parabola $${y^2} - 2x = 8y - 20,$$is (in sq. units)

The area of the triangle inscribed in the parabola $$y^2$$ = $$4x$$ , the ordinates of whose vertices are 1 , 2 and 4 is :

Let A(-4, 0) & B(4,0). Then the number of points C=(x,y) on the circle $${x^2} + {y^2} = 16$$ lying in first quadrant $$(x,y \geqslant 0)$$ such that the area of the triangle whose vertices are A,B,C is a integer is