Andhra Pradesh Board Solutions for Chapter: The Straight Line, Exercise 3: Exercise 3(c)

If non-zero numbers $a, b, c$ are in harmonic progression, then show that the equation $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$ represents a family of concurrent lines and find the point of concurrency.

Find the point on the straight line $3x+y+4=0$ which is equidistant from the points $(-5,6)$ and $(3,2)$.

A straight line through $P(3,4)$ makes an angle of $60°$ with the positive direction of the $X-$axis. Find the coordinates of the points on the line which are $5$ units away from $P$.

A straight line through $Q(\sqrt{3},2)$ makes an angle $\frac{\pi }{6}$ with the positive direction of the $X-$axis. If the straight line intersects the line $\sqrt{3}x-4y+8=0$ at $P$, find the distance $PQ$.

Show that the origin is within the triangle whose angular points are$(2,1), (3,-2)$ and $(-4,-1)$.

A straight line through $Q(2,3)$ makes an angle $\frac{3\pi }{4}$ with the negative direction of the $X-$axis. If the straight line intersects the line $x+y-7=0$ at $P,$ find the value of $k$ if  distance $PQ=\sqrt{k}$.          

Show that the straight lines $x+y=0, 3x+y-4=0$ and $x+3y-4=0$ form an isosceles triangle.

Find the area of the triangle formed by the straight lines $2x-y-5=0, x-5y+11=0$ and $x+y-1=0$.