Straight Lines

If $(-4,5)$ is one vertex and $7 x-y+8=0$ is one diagonal of a square, then the equation of second diagonal is

What is the interior angle of a regular octagon of side length 2 cm ?

If $\mathrm{P}=(3,12,4)$ and $\mathrm{Q}$ is a point on the line OP such that $O Q=3$ then the sum of all the coordinates of $Q$ is

The distance from the origin to the orthocentre of the triangle formed by the lines $x+y-1=0$ and $6 x^2-13 x y+5 y^2=0$ is

If the orthocenter of the triangle formed by the lines $2x+3y-1=0,x+2y+1=0$and $ax+by-1=0$ lies at origin, then$\frac{1}{a}+\frac{1}{b}=$

If $C$ is the mid-point of the line segment $\mathbf{A B}$ and $P$ is any point outside the line $A B$, then

In $\triangle A B C$, if $\mathrm{A}$ is $(1,2), \mathrm{B}$ and $\mathrm{C}$ lie on $\mathrm{y}=\mathrm{x}+\alpha$ (where $\alpha$ is variable), then the locus of the orthocenter of the triangle is

Let origin be the centroid of an equilateral triangle $\mathrm{ABC}$ and one of its sides be along the straight line $x+y=3$. If $\mathrm{R}$ and $\mathrm{r}$ are its circum radius and inradius respectively, then…

Suppose $\Delta\,ABC$is an isosceles triangle with $\angle\,C=90^{\circ},A=\left(2,3\right)$and $B=\left(4,5\right)$. Then the centroid of the triangle is

The equations of the perpendicular bisectors of the sides AB and AC of $\triangle \mathrm{ABC}$ are $x-y+5=0$ and $x+2 y=0$ respectively. If the coordinates of $A$ are $(1,-2)$, then the equation of the line $B C$ is

A straight line $\frac{x}{a}-\frac{y}{b}=1$ passes through the point $(8,6)$ and cuts a triangle of area 12 sq units from the axes of coordinates. The equations of the straight lines are

If a straight line perpendicular to $2 x-3 y+7=0$ forms a triangle with the co-ordinate axes whose area is 3 sq. units, then the equation of the straight line is :