Embibe Experts Solutions for Chapter: The Straight Line, Exercise 1: TS EAMCET 2018 (04-May Shift-1)

When the origin is shifted to $(-1, 2)$ by the translation of axes, the transformed equation of $x^2+y^2+2x-4y+1=0$ is

If a point $P(x, y)$ moves such that the sum of the squares of its coordinates is equal to their product, then the locus of $P$ excluding origin is

If the portion of a straight line intercepted between the coordinate axes is divided by the point $(2, 3)$ in the ratio $2 : 3$ then the product of the intercepts made by this line on the axes is

The slope of a line $L$ is $2.$ If $m_1, m_2$ are slopes of two lines which are inclined at an angle of $\frac{\pi }{6}$ with $L,$ then $m_1+m_2=$

In a $∆ABC, 2x+3y+1=0, x+2y-12=0$ are the perpendicular bisectors of its sides $AB$ and $AC$ respectively and if $A$ is $(3, 2),$ then the slope of the side $BC$ is

If the equation of a line having a slope $m (m\in Z),$ passing through $(1, 1)$ and making an angle of ${\tan }^{-1}\left(\frac{5}{7}\right)$ with the line $x+y-3=0$ is $ax+y+c=0,$ then $ac=$

$x-y=0$ and $\frac{x}{2}+\frac{y}{2}=1$ are respectively the perpendicular bisectors of the sides $AB$ and $AC$ of a triangle $ABC.$ If the vertex is $A\left(2, 3\right),$ then the equation of the side $BC$ is

In an isosceles right angled triangle, if the equation of the hypotenuse and its opposite vertex are $3x+4y=4$ and $\left(2, 2\right),$ then the slopes of the remaining two sides are