Straight Lines And Pair Of Straight Lines - Coordinate Geometry - Mathematics Previous Year Questions

The coordinates of the foot of the perpendicular drawn from the point (3, 4) on the line \(2x+y-7=0\) is

The slopes of the lines, which make an angle 45\(^\circ\) with the line \(3x-y=-5\), are

If two pairs of lines \(x^2-2mxy-y^2=0\) and \(x^2-2nxy-y^2=0\) are such that one of them represents the bisector of the angles between the other, then

If 3 and 4 are intercepts of a line L = 0, then the distance of L \(\equiv\) 0 from the origin is

The distance of the point (1, 2) from the line \(x+y+5=0\) measured along the line parallel to \(3x-y=7\) is equal to

Let the equation of the pair of lines \(y=p x\) and \(y=q x\) can be written as \((y-p x)(y-q x)=0\). Then the equation of the pair of the angle bisectors of the line \(x^2-4 x y-5 y^2=0\) is

The distance of the point \((1,2)\) from the line \(x+y+2=0\) measured along the line parallel to \(2 x-y=5\) is equal to

If 2 and 3 are intercepts of a line L = 0, then the distance of L \(\equiv\) 0 from the origin is

The slope of lines which makes an angle 45\(^\circ\) with the line \(2x-y=-7\)

In a \(\triangle A B C\), if coordinates of point \(A\) is \((1,2)\) and equation of the medians through \(B\) and \(C\) are \(x+y=5\) and \(x=4\) respectively, then the coordinates of \(B\) is

The ratio in which the line \(3 x+4 y+2=0\) divides the distance between the lines \(3 x+4 y+5=0\) and \(3 x+4 y-5=0\) is

What can be said regarding a line if its slope is negative?

For what value of \(\mathrm{a}\) and \(\mathrm{b}\) the intercepts cut off on the co-ordinate axes by the line \(a x-b y+8=0\) are equal in length but opposite in signs to those cut off by the line \(2 x-3 y+6=0\) on the axes

Let \(\mathrm{ABC}\) be a triangle with equations of its sides \(\mathrm{AB}, \mathrm{BC}\). \(\mathrm{CA}\) respectively are \(x-2=0, y-5=0\) and \(5 x+2 y-10=0\). Then the orthocentre of triangle lies on the line

The area of the triangle whose vertices are \((-2, a)(2,-6)\) and \((5,4)\) is 35 sq units then the value of '\(\mathrm{a}\)' is

The line joining two points \(A(2,0) B(3,1)\) is rotated about \(A\) in anticlockwise direction through an angle of \(15^{\circ}\). If \(B\) goes to \(C\) in the new position, then the coordinates of \(C\) is

The points on the \(x\)-axis whose perpendicular distance from the line \(\frac{x}{3}+\frac{y}{4}=1\) is 4 units are

Find the direction in which a straight line must be drawn through the point \((1,2)\) so that its point of intersection with the line \(x+y=4\) may be at a distance of \(\sqrt{\frac{2}{3}}\) from this point.

The perpendicular distance of a line from the origin is 5 units and its slope is \(-1\). The equation of the line is