Find the equation of the straight line which passes through the point \((1, -2)\) and cuts off equal intercepts from axes.
\(x + y + 1 = 0\)
Find the equation of the line passing through the point \((5, 2)\) and perpendicular to the line joining the points \((2, 3)\) and \((3, -1)\).
\(x - 4y + 3 = 0\)
Find the angle between the lines \(y = (2 - \sqrt{3})(x + 5)\) and \(y = (2 + \sqrt{3})(x - 7)\).
60° or 120°
Find the equation of the lines which pass through the point \((3, 4)\) and cut off intercepts from the coordinate axes such that their sum is 14.
\(x + y = 7\)
or
\(\dfrac{x}{6} + \dfrac{y}{8} = 1\)
Find the points on the line \(x + y = 4\) which lie at a unit distance from the line \(4x + 3y = 10\).
\((3, 1), (-7, 11)\)
Show that the tangent of an angle between the lines \(\dfrac{x}{a} + \dfrac{y}{b} = 1\) and \(\dfrac{x}{a} - \dfrac{y}{b} = 1\) is \(\dfrac{2ab}{a^2 - b^2}\).
\(\dfrac{2ab}{a^2 - b^2}\)
Find the equation of lines passing through \((1, 2)\) and making angle 30° with the y-axis.
\(y - \sqrt{3}x - 2 + \sqrt{3} = 0\)
Find the equation of the line passing through the point of intersection of \(2x + y = 5\) and \(x + 3y + 8 = 0\) and parallel to the line \(3x + 4y = 7\).
\(3x + 4y + 3 = 0\)
For what values of \(a\) and \(b\) are the intercepts cut off on the coordinate axes by the line \(ax + by + 8 = 0\) equal in length but opposite in signs to those cut off by the line \(2x - 3y + 6 = 0\)?
\(a = -\dfrac{8}{3},\ b = 4\)
If the intercept of a line between the coordinate axes is divided by the point \((-5, 4)\) in the ratio 1 : 2, then find the equation of the line.
\(8x - 5y + 60 = 0\)
Find the equation of a straight line on which the length of the perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of the x-axis.
\(\sqrt{3}x + y = 8\)
Find the equation of one of the sides of an isosceles right-angled triangle whose hypotenuse is given by \(3x + 4y = 4\) and the opposite vertex of the hypotenuse is \((2, 2)\).
\(x - 7y - 12 = 0\)