Intersection of Straight Lines

The straight lines $l_1$ and $l_2$ pass through the origin and trisect the line segment of the line $L:9x+5y=45$ between the axes. If $m_1$ and $m_2$ are the slopes of the lines $l_1$ and $l_2$, then the point of intersection of the line $y=(m_1+m_2)x$ with $L$ lies on

If the lines $y=3x+1$ and $2y=x+3$ are equally inclined to the line $y=mx+4$, then $m=$

If $\mathrm{P}\left(\mathrm{\theta }\right),\mathrm{Q}(\frac{\mathrm{\pi }}{2}+\mathrm{\theta })$ are tw points on the ellipse $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ and $\alpha$ is the angle between the normals $\mathrm{P} \mathrm{and} \mathrm{Q}$ then, 

Let $B\left(1,-3\right)$ and $D\left(0,4\right)$ represent two vertices of rhombus $ABCD$ in $\left(x,y\right)$ plane, then coordinate of vertex $A$ if $\angle BAD=60°$ can be equal to

The co-ordinates of the point where line $\frac{x}{a}+\frac{y}{b}=7$ intersects $y-\mathrm{axis}$ are

If $\theta$ is the acute angle between the lines $\frac{x}{a}+\frac{y}{b}=1,\frac{x}{b}+\frac{y}{a}=1$ then $\sin \theta =$

If the lines $L_1\equiv 2x+y+3=0,L_2\equiv kx+2y-3=0$ and $L_3\equiv 3x-2y+1=0$ are concurrent then the cosine of the acute angle between the lines $L_2=0$ and $2x-5y+7=0$ is

For $\alpha \in \left[0,\frac{\pi }{2}\right]$, the angle between the lines represented by $\left[x\cos \theta -y\right]\left[\left(\cos \theta +\tan \alpha \right)x-\left(1-\cos \theta ·\tan \alpha \right)y\right]=0$ is

If the lines $2x-3y+5=0,9x-5y+14=0$ and $3x-7y+\lambda =0$ are concurrent, then the value of $\lambda$ is equal to

If the line $y=mx+c$ is perpendicular to $y=1+x$ and passes through the point $\left(1,2\right)$, then the value of $c$ is equal to

The equation of the straight line parallel to $y=-3x$ and passing through the point $\left(3,-2\right)$ is

If the lines$\left.\begin{array}{r}\begin{array}{c}\lambda x+\left(\sin \alpha \right)y+\cos \alpha =0\\ x+\left(\cos \alpha \right)y+\sin \alpha =0\end{array}\\ x-\left(\sin \alpha \right)y+\cos \alpha =0\end{array}\right\}$ pass through the same point where $\alpha \in R$, then $\lambda$ lies in the interval

The equation of the perpendicular bisector of the line joining the points $A(2,3)$ and $B(6,-5)$ is

A line passes through the point $(2-5)$ and is parallel to the line $2x-3y=7$. The equation of the line is

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

If the line $x+3y+2=0$ and its perpendicular line are conjugate with respect to $3x^2-5y^2=15$, then the equation to conjugate line is

A line has the equation $5x+12y=18$ and other line has $4x+py=6$. If both lines are parallel to each other then find the value of p.

If the points $\left(-6,-4\right), (-3,2)$ and $(n,-5)$ are collinear points, then find the value of 'n'