Straight Lines ...

If $$a$$ and $$b$$ are real numbers between $$0$$ and $$1$$ such that the points $$(a,1),(1,b)$$ and $$(0,0)$$ from an equilateral triangle then the values of $$a$$ and $$b$$ respectively ?

$$x$$ co-ordinates of two points $$B$$ and $$C$$ are the roots of equation $$x^{2}+4x+3=0$$ and their $$y$$ co-ordinate are the roots of equation $$x^{2}-x-6=0$$. If $$x$$ co-ordinates of $$B$$ is less than $$x$$ co-ordinate of $$C$$ and $$y$$ co-ordinate of $$B$$ is greater than the $$y$$ co-ordinate of $$C$$ and co-ordinate of a third point $$A$$ be $$(3,-5)$$, find the length of the bisector of the interior angle at $$A$$ ?

The point whose abscissa is equal to its ordinate and which is equidistant from $$A(5,0)$$ and $$B(0,3)$$ is

The area of the triangle whose co-ordinates are $$(2012, 7), (2014, 7)$$ and $$(2014, a)$$ is $$1 \,sq$$ unit. The sum of possible values of $$a$$ is

If the points $$\left( {0,0} \right),\left( {3,\sqrt 3 } \right),\left( {p,q} \right)$$ form an equilateral triangle $$q_1, q_2$$ are the two values of $$q$$ then $$q_1 + q_2 = $$

The equation ot the line passing through the point $$( 1 , - 2,3 )$$ and parallel to the line$$x - y + 2 z = 5$$ and $$3 x + y + z = 6$$ is

If the line $$y= \sqrt{3x}$$ cuts the curve $$x^{4}+ax^{2}y+bxy+cx+dy+6=0$$ at $$A,B,C$$ and $$D$$, then $$OA.OB.OC.OD$$ is equal to ($$O$$ being origin)

ABC is an isosceles triangle with AB = AC, If the coordinates of the vertices of the base are B (1, 3) nd C(-2, 7), then the coordinates of the vertex A can be 

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 $$x =$$

the points on the cirve y={ x }^{ 3 }, the tangents at which are inclined at an angle $${ 60 }^{ 0 }$$ to x-axis is