Straight Lines and Pair of Straight Lines · Mathematics · COMEDK

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

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

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

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

Let the equation of pair of lines $$y=m_1 x$$ and $$y=m_2 x$$ can be written as $$\left(y-m_1 x\right)\left(y-m_2 x\right)=0$$. Then, the equation of the pair of the angle bisector of the line $$3 y^2-5 x y-2 x^2=0$$ is

The distance of the point $$(3,4)$$ from the line $$3 x+2 y+7=0$$ measured along the line parallel to $$y-2 x+7=0$$ is equal to

The slope of lines which makes an angle $$60^{\circ}$$ with the line $$y-3 x+18=0$$

3 and 5 are intercepts of a line $$L=0$$, then the distance of $$L=0$$ from $$(3,7)$$ 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

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

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

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

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

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

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

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

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

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

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