Slope of a Line

The vertices of a triangle $∆OBC$ are $O \left(0, 0\right), B\left(-3, -1\right), C\left(-1, -3\right)$ find the equation of the line parallel to $BC$ and intersecting the sides $OB \& OC$, whose perpendicular distance from the point $\left(0, 0\right)$ is half.

Find the inclination of a line $y=2$.

The angle between the line joining the points $(1,-2),(3,2)$ and the line $x+2y-7=0$ is

In the given figure, straight lines $\mathrm{AB}$ and $\mathrm{CD}$ intersect at $\mathrm{O}$. If $\mathrm{\delta }=3\mathrm{v}$, then $\angle \mathrm{v}=?$

The line $2x-y+1=0$ touches a circle at the point $\left(2,5\right)$ and the centre of the circle lies on $x-2y=4.$ The diameter (in units) of the circle is

The equation of the locus of the foot of perpendicular drawn from $\left(\mathrm{5,6}\right)$ on the family of lines $\left(x-2\right)+\lambda \left(y-3\right)=0$ (where $\lambda \in R$) is

The line $3x-4y+7=0$ is rotated through an angle $\frac{\pi }{4}$ in the clockwise direction about the point $\left(-1, 1\right).$ The equation of the line in its new position is

In a figure, $\mathrm{AB}\parallel \mathrm{BC}$ and $\angle \mathrm{AFE}={30}^{\mathrm{o}},$ then $\angle \mathrm{FCD}$ is

The nature of the angle between the tangents at any point $P$ and the line joining $P$ to origin $O$, where $P$ is a point on the curve $\mathrm{l}\mathrm{n}\left(x^2+y^2\right)=\mathrm{c }{\tan }^{-1}y/x,$ ($c$ is a constant), is

The slope of a line is double of the slope of another line. If tangent of the angle between them is $\frac{1}{3},$ find the slopes
of he lines.

What is the slope of the line perpendicular to the line passing through the points $(-5,1)$ and $(-2,0)$?

In the given figure, $AOB$ is a straight line, $\angle AOC =68°$ and $\angle BOC =x°$,The value of $x$:

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Let the sides of a triangle ABC are all integers with A as the origin. If (2, – 1) and (3, 6) are points on the line AB and AC respectively (lines AB and AC may be extended to contain these points), and lengths of any two sides are primes that differ by 50; compute the smallest possible value of the third side.

$AB$ is a straight line and $O$ is point on the line $AB$. If one draws a line $OC$ not coinciding with $OA$ or $OB$, then the $\angle AOC$ and $\angle BOC$ are

The value of $k>0$such that the angle between the lines $4x-y+7=0$ and $kx-5y-9=0$ is $45°$ is

The measure of the angle between pair of lines $x=y$ and $y=0$ is?

If the lines $kx-2y-1=0$ and $6x-4y-m=0$ are identical (co -incident) lines, then the values of $k$ and $m$ are ......

If a chord of a rectangular hyperbola, parallel to its conjugate axis subtends angles ${\theta }_1 and {\theta }_2$ at its vertices, then

If the line passing through $\left(4,\mathrm{ }3\right)$ and $\left(2,\mathrm{ }\mathrm{k}\right)$ is perpendicular to $\mathrm{y}=2\mathrm{x}+3$ , then $\mathrm{k}=$