Tamil Nadu Board Solutions for Chapter: Two Dimensional Analytical Geometry, Exercise 4: Exercise

Find the separate equation of the following pair of straight lines $3x^2+2xy-y^2=0$.

Find the separate equation of the following pair of straight lines $6(x-1{)}^2+5(x-1\left)\right(y-2)-4(y-2{)}^2=0$.

Find the separate equation of the pair of straight lines $2x^2-xy-3y^2-6x+19y-20=0$

Find $p$ and $q,$ if the following equation represents a pair of perpendicular lines $6x^2+5xy-p{y}^2+7x+qy-5=0$

Find the value of $k,$ if the equation $12x^2+7xy-12y^2-x+7y+k=0$ represents a pair of straight lines. Further, find whether these lines are parallel or intersecting.$$

For what value of $k$ does the equation $12x^2+2kxy+2y^2+11x-5y+2 = 0$ represent two straight lines.

Show that the equation $9x^2-24xy+16y^2-12x+16y-12 = 0$ represents a pair of parallel lines. Find the distance between them.

Show that the equation $4x^2+4xy+y^2-6x-3y-4=0$ represents a pair of parallel lines. Find the distance between them.