Straight Lines ...

The locus of a point, whose abscissa and ordinate are always equal is:

Find the equation of the line passing through \((-3,5)\) and perpendicular to the line through the points \((2,5)(-3,6)\).

Find the equation of line passing through \((h, 0)\) and \((0, k)\) and divided by the point \((1,2)\) in the ratio \(2: 3\):

What is the distance of (5, 12) from origin?

Find the values of \(k\) for which the length of the perpendicular from the point \((4,1)\) on the line \(3 x-4 y+k=0\) is 2 units?

What is the equation of the straight line which passes through the point of intersection of the straight lines \(x+2 y=5\) and \(3 x+7 y=17\) and is perpendicular to the straight line \(3 x+4 y=10 ?\)

Find the equation of the line perpendicular to the line \(x-3 y+5=0\) and passes through the point \((2,-4)\).

The equation of the line passing through the point \((2,3)\) and the point of intersection of lines \(2 x-3 y+7=\) 0 and \(7 x+4 y+2=0\) is:

Find the value of \(k\) for which the distance of point \((k+2,2 k+3)\) is \(\frac{4}{ \sqrt{10}}\) from the line \(x+\) \(3 y=7 ?\)

The angle between the lines \(x+y-3=0\) and \(x-y+3=0\) is \(\alpha\) and the acute angle between the lines \(x\) -\(\sqrt{3} y+2 \sqrt{3}=0\) and \(\sqrt{3} x-y+1=0\) is \(\beta\). Which one of the following is correct?