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

If $P\left(1+\frac{t}{\sqrt{2}},2+\frac{t}{\sqrt{2}}\right)$ be any point on a line, then the range of the values of $t$ for which the point $P$ lies between the parallel lines $x+2y=1$ and $2x+4y=15$ is

The locus of circumcentre of the triangle formed by vertices $A\left(\left(-pq-p-q\right),-\left(1+p\right)\left(1+q\right)\right), B\left(pq+p-q,\left(1+p\right)\left(1+q\right)\right), C\left(pq+q-p,\left(1+p\right)\left(1+q\right)\right)$ is

Let two sides of rectangle of area $20$ sq. units are along lines $x-y=0$ and $x+y=2,$ then the locus of point of intersection of diagonals is:

Equation of the line pair through the origin and perpendicular to the line pair $xy-3y^2+y-2x+10=0$ is

Let $u\equiv ax+by+a\sqrt[3]{b}=0, v\equiv bx-ay+b\sqrt[3]{b}=0,$ where $a,b\in R$ be two straight lines, then find the equations of the bisectors of the angles formed by $k_{1}u-k_{2}v=0 \& k_{1}u+k_{2}v=0$ for non zero real $k_1 \& k_2$.

The line $l_1$ passing through the point$(1,1)$ and the $l_2$ passes through the point $(-1,1)$ . If the difference of the slope of lines is $2 .$ Find the locus of the point of intersection of the $l_1$ and $l_2$ .

The two lines pairs $y^2-4y+3=0$ and $x^2+4xy+4y^2-5x-10y+4=0$ enclose a $4$ sided convex polygon, then the correct statement among the following is/are

If the distance between the lines represented $9x^2-24xy+16y^2+k(6x-8y)=0$ is $4,$ then $k$ may be