Odisha Board Solutions for Chapter: Straight Lines, Exercise 2: EXERCISES 11 (b)

Obtain the equation of straight line: passing through the points $(2,3)\text{ and }(-4,1)$.

Prove that a pair of lines through origin perpendicular to the pair of lines represented by $p{x}^2+2qxy+r{y}^2=0$ is given by $r{x}^2-2qxy+p{y}^2=0$.

Obtain the condition that a line of the pair of lines $a{x}^2+2hxy+b{y}^2=0$ which is coincides with a line of pair of lines $p{x}^2+2qxy+r{y}^2=0$.

If the pair of lines represented $x^2-2pxy-y^2=0\text{ and }{x}^2-2qxy-y^2=0$ be such that each pair bisects the angle between the other pair, then prove that $pq=-1$.

Transform the equation $x^2+y^2-2x-4y+1=0$ by shifting the origin to $(1,2)$ and keeping the axes parallel.

Transform the equation $2x^2+3y^2+4xy-12x-14y+20=0$, when referred to parallel axes through $(2,1)$.

Find measure of rotation so that the equation $x^2-xy+y^2=5$ when transformed does not contain $xy-$term.

What does the equation $x+2y-10=0$ become when the origin is changed to $(4,3) ?$