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-

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 :

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

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

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

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