## Polar and Cartesian Coordinates

### Cartesian co-ordinates of a point

This is the most popular co-ordinate system.

**Axis of x:** The line XOX’ is called axis of x.

**Axis of y:** The line YOY’ is called axis of y.

**Co-ordinate axes:** x axis and y axis together are called axis of co-ordinates or axes of reference.

**Origin:** The point ‘O’ is called the origin of co-ordinates or the origin.

Let OL = x and OM = y which are respectively called the abscissa (or x-coordinate) and the ordinate (or y-coordinate). The co-ordinate of P are (*x, y*).

Here, co-ordinates of the origin is (0, 0). The y co-ordinates of every point on x-axis is zero.

The x co-ordinates of every point on y-axis is zero.

**Oblique axes:** If both the axes are not perpendicular then they are called as oblique axes.

### Polar co-ordinates

Let OX be any fixed line which is usually called the initial line and O be a fixed point on it. If distance of any point P from the O is ‘r’ and *∠XOP* *=* *θ*, then (*r, θ* ) are called the polar co-ordinates of a point P.

### To convert from Polar Coordinates (*r,θ*) to Cartesian Coordinates (*x,y*):

If (*x, y*) are the cartesian co-ordinates of a point P, then ** x = r cos θ**;

**; and**

*y = r sin θ*