Subject Experts Solutions for Chapter: Coordinate System and Straight Lines, Exercise 1: Practice Exercise

The area of the figure formed by the lines $ax+by+c=0, ax-by+c=0, ax+by-c=0$ and $ax-by-c=0$ is

The three lines $4x+4y=1, 8x-3y=2, y=0$ are

The line $3x+4y-24=0$ intersects the $X-$axis at $A$ and $Y-$axis at $B.$ Then, the circumcentre of the $△OAB,$ where $O$ is the origin, is 

The product of perpendiculars from the two points $(\pm 4, 0)$ to the line $3x\cos \varphi +5y\sin \varphi =15$ is

Two straight lines passing through the point $A(3,2)$ cut the line $2y=x+3$ and $X$-axis perpendicularly at $P$ and $Q,$ respectively. The equation of the line $PQ$ is

A straight line intersects $X$ and $Y-$axes at $P$ and $Q,$ respectively. If $\left(3,5\right)$ is the middle point of $PQ,$ then what is the area of the $∆OPQ?$

$(a,2b)$ is the midpoint of the line segment joining the points $\left(10,-6\right)$ and $(k,4).$ If $a-2b=7,$ then what is the value of $k?$

What is the acute angle between the lines represented by the equations $y-\sqrt{3}x-5=0$ and $\sqrt{3}y-x+6=0?$