Andhra Pradesh Board Solutions for Chapter: Pair of Straight Lines, Exercise 3: Exercise 4(c)

Find the combined equation of the lines joining the origin to the points of intersection of $x^2+y^2=1$ and $x+y-1$.

Find the angle between the lines joining the origin to the points of intersection of $y^2=x$ and $x+y=1$.

Show that the lines joining the origin to the points of intersection of the curve $x^2-xy+y^2+3x+3y-2=0$ and the straight line $x-y-\sqrt{2}=0$ are mutually perpendicular.

Find the values of $k$, if the lines joining the origin to the points of intersection of the curve $2x^2-2xy+3y^2+2x-y-1=0$ and the line $x+2y=k$ are mutually perpendicular.

Find the angle between the lines joining the origin to the points of intersection of the curve $x^2+2xy+y^2+2x+2y-5=0$ and the line $3x-y+1=0$.

Find the condition for the chord $lx+my=1$ of the circle $x^2+y^2=a^2$ (whose centre is the origin) to subtend a right angle at the origin.

Find the condition for the lines joining the origin to the points of intersection of the circle $x^2+y^2=a^2$ and the line $lx+my=1$ to coincide.

Write down the equation of the pair of straight lines joining the origin to the points of intersection of the line $6x-y+8=0$ with the pair of straight lines

$3x^2+4xy-4y^2-11x+2y+6=0$. Show that the lines so obtained make equal angles with the coordinate axes.