Straight Lines ...

If the slop of one of the lines represented by $$ax^2-6xy+y^2=0$$ is the square of the other,then the value of a is

Let $$A=(a_1, a_2)$$ and $$B=(b_1, b_2)$$ be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between A and B?

If the straight line $$ax + by + p = 0$$ and $$x\cos \alpha + y \sin \alpha = p$$ enclosed an angle of $$\dfrac {\pi}{4}$$ and the line $$x\sin \alpha - y \cos \alpha = 0$$ meets them at the same point, then $$a^{2} + b^{2}$$ is

The distance of the point $$A(a, b, c)$$ from the x-axis is

$$ABC$$ is an isosceles triangle. If the coordinates of the base are $$B(1,3)$$ and $$C(-2,7)$$. The vertex $$A$$ can be

How many points $$(x, y)$$ with integral co-ordinates are there whose distance from $$(1, 2)$$ is two units?

The distance between the points $$\left( a\cos { { 48 }^{ o } } ,0 \right) $$ and $$\left( 0,a\cos { { 12 }^{ o } }  \right) $$ is $$d$$ then $${ d }^{ 2 }{ a }^{ 2 }=$$

The point $$P\left( x,y \right)$$ is equidistant from the points $$Q\left( c+d,d-c \right)$$ and $$R\left( c-d,c+d \right)$$ then

The angle between the pair of lines whose equation is $$4{ x }^{ 2 }+10xy+m{ y }^{ 2 }+5x+10y=0$$ is

Points $$A\left( 3,2,4 \right) ,B\left( \cfrac { 33 }{ 5 } ,\cfrac { 28 }{ 5 } ,\cfrac { 38 }{ 5 }  \right) $$, and $$C(9,8,10)$$ are given. The ratio in which $$B$$ divides $$\overline { AC } $$ is