## Coordinate Geometry

### 1. Straight Line

**Parametric form of line**

**Question 1.**

The line joining the point $A(2,0)$ and $B(4,2)$ is rotated about A by an angle $15^0$. If in new position B reaches to C. Find possible co-ordinates of C.

**Question 2.**

The distance between two parallel lines is unity. A point P lies between the lines at a distance ‘a’ from one of them. Find the length of side of an equilateral triangle PQR, vertex Q of which lies on one ot the parallel lines and vertex R lies on the other line.

**Question 3.**

Find the equation of line passing through $P(1,2)$ and cutting the line $x+y=5$ and $2x-y=7$ at A and B respectively. Such that Harmonic mean of PA and PB is 10.

**Question 4.**

A square lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha$ where $\alpha \,\in\,(o,\cfrac{\pi}{4})$ with the positive direction of x-axis. Find the equation of its diagonals ( given length of side of square is ‘a’ ).

**Question 5.**

A straight line is such that its segment between tines $5x-y-4=0$ and $3x+4y-4=0$ is bisected at the point $(1,5)$. Find its equation.

**Position of points with respect to the line.**

**Question 1.**

Find range of $\theta$ if point $P(Sin\theta , Cos\theta )$ where $\theta \,\in\, [0,2\pi]$ lie inside the triangle whose vertices are $(0,0)$, $(\sqrt{\cfrac{3}{2}},0)$ and $(0,\sqrt{\cfrac{3}{2}})$.

**Question 2.**

Determine the value of $\alpha$ for which the point $(\alpha , \alpha^2)$ lie inside the triangle formed by the lines $2x+3y-1=0$, $x+2y-3=0$ and $5x-6y-1=0$