Embibe Experts Solutions for Chapter: Point and Straight Line, Exercise 2: Level 2

Let $ABC$ be a triangle. Let $A$ be the point $\left(1,2\right), y=x$ be the perpendicular bisector of $AB$ and $x-2y+1=0$ be the angle bisector of $\angle C$. If equation of $BC$ is given by $ax+by-5=0$, then the value of $a+b$ is

A point $P(h, k)$ lies on the straight line $x+y+1=0$ and is at a distance $5$ units from the origin. If $k$ is negative, then $h$ is equal to

What is the product of the perpendiculars drawn from the points $\left(\pm \sqrt{a^2-b^2},0\right)$ upon the line $bx\cos \alpha +ay\sin \alpha =ab$?

Two straight lines passing through the point $A(3,2)$ cut the line $2y=x+3$ and $X$-axis perpendicularly at $P$ and $Q,$ respectively. The equation of the line $PQ$ is

What is the angle between the straight lines $\left(m^2-mn\right)y=\left(mn+n^2\right)x+n^3$ and $\left(mn+m^2\right)y=\left(mn-n^2\right)x+m^3,$ where $m>n?$

The equation of perpendicular bisector of the sides $AB$ and $AC$ of a $∆ABC$ are $x-y+5=0$ and $x+2y=0,$ respectively. If the point $A$ is $\left(1,-2\right),$ then the equation of line $BC$ is

If the curve $x^2+2y^2=2$ intersects the line $x+y=1$ at two points $P$ and $Q$, then the angle subtended by the line segment $PQ$ at the origin is

Let the equation of the pair of lines, $y=px$ and $y=qx,$ can be written as $\left(y-px\right)\left(y-qx\right)=0.$ Then the equation of the pair of the angle bisectors of the lines $x^2-4xy-5y^2=0$ is: