Andhra Pradesh Board Solutions for Chapter: Pair of Straight Lines, Exercise 2: Exercise 4(b)

Show that the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+2y-8=0$ are concurrent.

Find the distance between the pairs of parallel straight lines $9x^2-6xy+y^2+18x-6y+8=0$.

Find the distance between the pairs of parallel straight lines $x^2+2\sqrt{3}xy+3y^2-3x-3\sqrt{3}y-4=0$.

Show that the two pairs of lines $3x^2+8xy-3y^2=0$ and $3x^2+8xy-3y^2+2x-4y-1=0$ form a square.

Find the product of the lengths of the perpendiculars drawn from $(2,1)$ upon the lines $12x^2+25xy+12y^2+10x+11y+2=0$.

Show that the straight lines $y^2-4y+3=0$ and $x^2+4xy+4y^2+5x+10y+4=0$ form a parallelogram and find the lengths of its sides.

Show that the product of the perpendicular distances from the origin to the pair of straight lines represented by $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ is $\frac{\left|c\right|}{\sqrt{(a-b{)}^2+4h^2}}$.

If the equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ represents a pair of intersecting lines, then show that the square of the distance of their point of intersection from the origin is $\frac{c(a+b)-f^2-g^2}{ab-h^2}$. Also show that the square of this distance is $\frac{f^2+g^2}{h^2+b^2}$ if the given lines are perpendicular.