Find the equation of the straight line which passes through the point $(1-2)$ and cuts off equal intercepts from axes.

Find the equation of the line passing through the point $(5,2)$ and perpendicular to the line joining the points $(2,3)$ and $(3,-1)$.

Find the angle between the lines $y=(2-\sqrt{3})(x+5)$ and $y=(2+\sqrt{3})(x-7)$.

Find the equation of the lines which passes through the point $(3,4)$ and cuts off intercepts from the coordinate axes such that their sum is 14 .

Find the points on the line $x+y=4$ which lie at a unit distance from the line $4 x+3 y=10$

Show that the tangent of an angle between the lines $\frac{x}{a}+\frac{y}{b}=1$ and $\frac{x}{a}-\frac{y}{b}=1$ is $\frac{2 a b}{a^2-b^2}$

Find the equation of lines passing through $(1,2)$ and making angle $30^{\circ}$ with $Y$-axis.

Find the equation of the line passing through the point of intersection of $2 x+y=5$ and $x+3 y+8=0$ and parallel to the line $3 x+4 y=7$.

For what values of $a$ and $b$ the intercepts cut off on the coordinate axes by the line $a x+b y+8=0$ are equal in length but opposite in signs to those cut off by the line $2 x-3 y+6=0$ on the axes?

If the intercept of a line between the coordinate axes is divided by the point $(-5,4)$ in the ratio $1: 2$, then find the equation of the line.

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of $120^{\circ}$ with the positive direction of $X$-axis.

Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by $3 x+4 y=4$ and the opposite vertex of the hypotenuse is $(2,2)$.

If the equation of the base of an equilateral triangle is $x+y=2$ and the vertex is $(2,-1)$, then find the length of the side of the triangle.

A variable line passes through a fixed point $P$. The algebraic sum of the perpendiculars drawn from the points $(2,0),(0,2)$ and $(1,1)$ on the line is zero. Find the coordinates of the point $P$.

In what direction should a line be drawn through the point $(1,2)$, so that its point of intersection with the line $x+y=4$ is at a distance $\frac{\sqrt{6}}{3}$ from the given point?

A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.

Find the equation of the line which passes through the point $(-4,3)$ and the portion of the line intercepted between the axes is divided internally in the ratio $5: 3$ by this point.

Find the equations of the lines through the point of intersection of the lines $x-y+1=0$ and $2 x-3 y+5=0$ and whose distance from the point $(3,2)$ is $\frac{7}{5}$.

If the sum of the distance of a moving point in a plane from the axes is 1, then find the locus of the point.

$P_1$ and $P_2$ are points on either of the two lines $y-\sqrt{3}|x|=2$ at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from $P_1, P_2$ on the bisector of the angle between the given lines.

If $p$ is the length of perpendicular from the origin on the line $\frac{x}{a}+\frac{y}{b}=1$ and $a^2, p^2$ and $b^2$ are in AP, the show that $a^4+b^4=0$.

Match the following.

The value of the $\lambda$, if the lines $(2+3 y+4)+\lambda(6 x-y+12)=0$ are

The equation of the line through the intersection of the lines $2 x-3 y=0$ and $4 x-5 y=2$ and

A line cutting off intercept -3 from the $Y$-axis and the tangent at angle to the $X$-axis is $\frac{3}{5}$, its equation is

Slope of a line which cuts off intercepts of equal lengths on the axes is

The equation of the straight line passing through the point $(3,2)$ and perpendicular to the line $y=x$ is

The equation of the line passing through the point $(1,2)$ and perpendicular to the line $x+y+1=0$ is

The tangent of angle between the lines whose intercepts on the axes are $a,-b$ and $b,-a$ respectively, is

If the line $\frac{x}{a}+\frac{y}{b}=1$ passes through the points $(2,-3)$ and $(4,-5)$, then $(a, b)$ is

The distance of the point of intersection of the lines $2 x-3 y+5=0$ and $3 x+4 y=0$ from the line $5 x-2 y=0$ is

The equation of the lines which pass through the point $(3,-2)$ and are inclined at $60^{\circ}$ to the line $\sqrt{3} x+y=1$ is

The equations of the lines passing through the point $(1,0)$ and at a distance $\frac{\sqrt{3}}{2}$ from the origin, are

The distance between the lines $y=m x+c_1$ and $y=m x+c_2$ is

The coordinates of the foot of perpendiculars from the point $(2,3)$ on the line $y=3 x+4$ is given by

If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is $(3,2)$, then the equation of the line will be

Equation of the line passing through $(1,2)$ and parallel to the line $y=3 x-1$ is

Equations of diagonals of the square formed by the lines $x=0, y=0, x=1$ and $y=1$ are

For specifying a straight line, how many geometrical parameters should be known?

The point $(4,1)$ undergoes the following two successive transformations

(i) Reflection about the line $y=x$

(ii) Translation through a distance 2 units along the positive $X$-axis.

Then, the final coordinates of the point are

A point equidistant from the lines $4 x+3 y+10=0,5 x-12 y+26=0$ and $7 x+24 y-50=0$ is

A line passes through $(2,2)$ and is perpendicular to the line $3 x+y=3$. Its $y$-intercept is

The ratio in which the line $3 x+4 y+2=0$ divides the distance between the lines $3 x+4 y+5=0$ and $3 x+4 y-5=0$ is

One vertex of the equilateral triangle with centroid at the origin and one side as $x+y-2=0$ is

If $a, b$ and $c$ are in AP, then the straight lines $a x+b y+c=0$ will always pass through .............. .

The line which cuts off equal intercept from the axes and pass through the point $(1,-2)$ is ............ .

Equation of the line through thes point $(3,2)$ and making an angle of $45^{\circ}$ with the line $x-2 y=3$ are ........... .

The points $(3,4)$ and $(2,-6)$ are situated on the ............. of the line $3 x-4 y-8=0$.

A point moves so that square of its distance from the point $(3,-2)$ is numerically equal to its distance from the line $5 x-12 y=3$. The equation of its locus is ̣........... .

Locus of the mid-points of the portion of the line $x \sin \theta+y \cos \theta=p$ intercepted between the axes is $\ldots \ldots \ldots .$.

If the vertices of a triangle have integral coordinates, then the triangle cannot be equilateral.

The points $A(-2,1), B(0,5)$ and $C(-1,2)$ are collinear.

Equation of the line passing through the point $\left(a \cos ^3 \theta, a \sin ^3 \theta\right)$ and perpendicular to the line $x \sec \theta+y \operatorname{cosec} \theta=a$ is $x \cos \theta-y \sin \theta=a \sin 2 \theta$.

The straight line $5 x+4 y=0$ passes through the point of intersection of the straight lines $x+2 y-10=0$ and $2 x+y+5=0$.

The vertex of an equilateral triangle is $(2,3)$ and the equation of the opposite side is $x+y=2$. Then, the other two sides are $y-3=(2 \pm \sqrt{3})(x-2)$.

The equation of the line joining the point $(3,5)$ to the point of intersection of the lines $4 x+y-1=0$ and $7 x-3 y-35=0$ is equidistant from the points $(0,0)$ and $(8,34)$.

The line $\frac{x}{a}+\frac{y}{b}=1$ moves in such a way that $\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{c^2}$, where $c$ is a constant. The locus of the foot of the perpendicular from the origin on the given line is $x^2+y^2=c^2$.

The lines $a x+2 y+1=0, \quad b x+3 y+1=0$ and $c x+4 y+1=0$ are concurrent, if $a, b$ and $c$ are in GP.

Line joining the points $(3,-4)$ and $(-2,6)$ is perpendicular to the line joining the points $(-3,6)$ and $(9,-18)$.