Straight Lines ...

If the equation $$ax^{2}-6xy+y^{2}  + 2gx+2fy+c=0$$ represents a pair of line whose slopes are $$m$$ and $$m^{2}$$, then sum of all possible values of $$a$$  is-

The diagonal passing through origin of a quadrilateral formed by $$x=0, y=0, x+y=1 $$ and $$6x+y=3$$ is

If the line $$3x-y+1=0$$ and  $$x-2y+3=0$$ are equally inclined to the line $$y=mx$$, then the value of $$m$$ is given by

The shortest distance of the point $$(h,k)$$ from both the axes are

One vertex of a square $$ABCD$$ is $$A(-1, 1)$$ and the equation of one diagonal $$BD$$ is $$3x+y-8=0$$ then $$C$$=

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

The area of the triangle vertices $$(1,0),(7,0)$$ and $$(4,4)$$ is ___ square units.

A triangle with vertices $$(4,0),(-1,-1),(3,5)$$ is:

If in a parallelogram $$ABCD$$, the coordinate of $$A, B$$ and $$C$$ are respectively $$(1, 2), (3, 4)$$ and $$(2, 5)$$, then the equation of the diagonal $$BD$$ is:-

In the given figure (not drawn to scale), the coordinates of P, Q and R are (3, 0) (0, 5) and (0, -5) respectively. Find the area of $$\Delta PQR$$.