Straight Lines ...

if the points A(z),B(-z) and C(z+1) are vertices of an equilateral triangle then ---- test question

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-

Two sides of a rhombus are along the lines, $$x-y+1=0$$ and $$7x-y-5=0$$. If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus?

If three lines $$x-3y=p,ax+2y=q$$ and $$ax+y=r$$ form a right angled triangle, then 

If the tangent at $$\theta =\frac { \pi  }{ 4 } $$ to the curve $$x=a\cos ^{ 3 }{ \theta  } ,y=a\sin ^{ 3 }{ \theta  } $$ meets the x and y axes in A and B then the area of the triangle OAB is

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 $$ - $$

If the area of triangle formed by the points (2a , b) (a + b , 2b + a) and (2b , 2a) be $$\lambda$$ , then the area of the triangle whose vertices are (a + b , a b) , (3b a , b + 3a) and (3a b , 3b a) will be

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