Lecture 3 Coordinate Geometry Yaindrila Barua Lecturer GED

Lecture 3 Coordinate Geometry Yaindrila Barua Lecturer, GED (Mathematics)

Coordinate System 1. Cartesian Coordinate System (x, y) 2. Polar Coordinate System

We can covert coordinate system

Cartesian to Polar: 1. (2, 3) to Polar Coordinate. Here, x=2 and y=3 Polar

Polar to Cartesian Coordinate System Convert into Cartesian (x, y)=(-2, -2)

Linear Equation Non-Linear Equation ax+by=c

Changes of Axes Translation of axes Rotation of axes Translation- Rotation

Translation of Axes Then new x=x`+h New y= y`+k

(1, 1) is a point After changing the origin (1, 1) point will be change. Locate the point (1, 1) when origin Is transferred to the point (2, -1) New x=1+2 =3 New y=1+(-1)=0 (1, 1) O (0, 0) (3, 0) will be the new point (2, -1)

Origin is transferred to the point (h, k)=(2, -1) so as the transferred relations are X=x’+h=x’+2 and Y=y’+k = y’-1. Using the above information given equation (1) becomes, X=x’+2 and y=y’ 1

Removing suffices from the above equation we get the transformed equation of. the given curve This is the required equation that represents an ellipse.