Various Forms of the Equation of a Line

The equation of a straight line passing through the intersection of the lines $x+y+1=0$, $2x-y+5=0$ and through the point $(5,-2)$.

In the gradient-intercept form of equation $y = mx + c$, the point where line cuts $y$-axis is:

The equation of the image of the line $x+2=0$ with respect to $x=0$ is

If a line passes through point $A(0,c)$ and has gradient $\text{'}m\text{'}$ then the equation will be:

Find the equation of a straight line which is parallel to the line $3x-4y=12$ and passes through the point $\left(6,4\right).$

If $3x-4y+7=0$ and $ax+2y+1=0$ are perpendicular, then $\text{'}a\text{'}$ equal to:

If the point $\left(\alpha , \frac{7\sqrt{3}}{3}\right)$ lies on the curve traced by the mid-points of the line segments of the lines $x \cos \theta +y\sin \theta =7, \theta \in \left(0, \frac{\mathrm{\pi }}{2}\right)$ between the co-ordinates axes, then $\alpha$ is equal to

A straight line $AB$ cuts the co-ordinate axes at $A$ and $B.$ If the mid-point of $AB$ is $\left(2,3\right),$ find the equation of $AB.$

A straight line cuts off the intercepts $OA=a$ and $OB=b$ on the positive direction of $x-$axis and $y-$axis respectively. If the perpendicular from origin to this line makes an angle $\frac{\mathrm{\pi }}{6}$ with positive direction of $y-$axis and are of $∆OAB$ is $\frac{98}{3}\sqrt{3}$ sq. units, then $a^2-b^2$ is equal to

A straight line $\mathrm{AB}$ cuts the co-ordinate axes at $\mathrm{A}$ and $\mathrm{B}$. If the midpoint of $\mathrm{AB}$ is $\left(2, 3\right)$, find the equation of $\mathrm{AB}$.

A straight line $\mathrm{AB}$ cuts the co-ordinate axes at $\mathrm{A}$ and $\mathrm{B}$. If the midpoint of $\mathrm{AB}$ is $\left(2, 3\right)$, find the equation of $\mathrm{AB}$.

Write the equation of the lines for which $\tan \theta =\frac{1}{2}$, where $\theta$ is the inclination of the line and $x$-intercept is $4$.

Show that two lines $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$, where $b_1, b_2\ne 0$ are perpendicular if $a_1{a}_2+b_1{b}_2=0$.

Equation of a line is $3x-4y+10=0$. Find its $x$-and $y$-intercepts.

Consider a parallelogram whose sides are represented by the lines $2x+3y=0, 2x+3y-5=0, 3x-4y=0$ and $3x-4y=3$. The equation of the diagonal not passing through the origin is

The slope of a line joining the points $\left(2,k\right)$ and $\left(-4,2\right)$ is $\frac{1}{2},$ then find $\text{'}k\text{'}.$

Find the equation of the normal to the curve $y=x^2+4x+1$ at the point $\left(3,22\right)$. if slope of tangent is $10$.

If the triangle with vertices $A\equiv \left(2,3\right), B\equiv \left(4,-1\right)$ and $C\equiv \left(-1,2\right)$, then the equation of median from $A$ is