Straight Lines

$Statement- 1$: If the general equation $x^{2}+y^{2}+2 x y+2 g x+2 f y+4=0$ represents a pair of real lines then $|\mathrm{g}| \geq 2$. $Statement- 2$: The equation $a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+c=0$ represents…

The equation $x^{2}-2 \sqrt{3} x y+3 y^{2}-3 x+3 \sqrt{3} y-4=0 \quad$ represents

If \(\int_0^n[x] \mathrm{dx}=66\), then \(n=\)

The locus of the point of intersection of the lines $x=a\left(\frac{1-t^2}{1+t^2}\right)$ and $y=\frac{2 a t}{1+t^2}$ represent $(t$ being a parameter)

The distance from the origin to the image of $(1$, 1) with respect to the line $x+y+5=0$ is

If the coordinates of the points $A$ and $B$ be $(3,3)$ and $(7,6)$, then the length of the portion of the line $\mathrm{AB}$ intercepted between the axes is

What is the angle between the two straight lines $y=(2-\sqrt{3}) x+5$ and $y=(2+\sqrt{3}) x-7 ?$

The points $(0,7,10),(-1,6,6)$ and $(-4,9,6)$ form

The distance between the parallel lines $3 x-4 y+7=0$ and $3 x-4 y+5=0$ is $\frac{a}{b}$. Value of $a+b$ is

The larger of two angles made with the $X$-axis of a straight line drawn through $(1, 2)$ so that it intersects the line $x+y=4$ at a point distant $\sqrt{6}/3$ from the point $(1, 2)$ is

Two equal sides of an isosceles triangle are $7x-y+3=0$ and $x+y-3=0$ and its third side passes through the point $(1, -10)$. The equation of the third side is

A ray of light coming from the point (1,2) is reflected at a point A on the $x$ -axis and then passes through the point $(5,3) .$ The co-ordinates of the point $A$ is