 Hello and welcome to the session. In this session we are going to discuss change of axis, transformation formula, let O with the coordinate 00 be origin and with respect to O, OX and OY be the original axis. Here O is the origin with the coordinate 00 and with respect to O, OX and OY are the original axis. Let O' be the new origin and HK are its coordinates with respect to OX and OY. Let O' is the new origin with the coordinate HK with respect to OX and OY. Let O' be drawn parallel to OX and in the direction similar to OX and O' be drawn parallel to OY and in the direction of OY. Let the coordinates of the point P be XY refer to the axis OX and OY, X' Y' be its coordinates with respect to new pair of axis O' X' and O' Y' Let O' R and PQ be the perpendicular drawn from O' and P respectively to the X axis. Let PQ meet O' X' at point Q' Then X is equal to OQ which is equal to OR plus RQ that is H plus X' and Y is equal to QP which is equal to QQ dash plus Q dash P that is K plus Y dash. Then we have X is equal to OQ which is equal to OR plus RQ that is H plus X' which is equal to X' plus H and Y is equal to QP which is equal to QQ dash plus Q dash P that is K plus Y dash OR can be written as Y' plus K and equation in X and Y is transformed into an equation in X' and Y' by replacing X by X' plus H and Y by Y' plus K This transformation is called translation of axis. Let us take an example, transform X square plus Y square minus of 3X minus of 5Y plus 2 is equal to 0 to the parallel axis through 3 by 2, 5 by 2 The given equation is X square plus Y square minus of 3X minus of 5Y plus 2 is equal to 0 and we need to transform X square plus Y square minus of 3X minus of 5Y plus 2 is equal to 0 to the parallel axis through the given point that is 3 by 2, 5 by 2 Therefore we put X is equal to X dash plus 3 by 2 and Y is equal to Y dash plus 5 by 2 in the above equation and we get X dash plus 3 by 2 the whole square plus Y dash plus 5 by 2 the whole square minus of 3 into X dash plus 3 by 2 minus of 5 into Y dash plus 5 by 2 plus 2 is equal to 0 which implies that X dash plus 3 by 2 the whole square can be written as X dash square plus 9 upon 4 plus 3 into X dash plus Y dash plus 5 by 2 the whole square can be written as Y dash square plus 25 by 4 plus 5 into Y dash minus of 3 into X dash is equal to minus 3 X dash minus of 3 into 3 by 2 is equal to minus of 9 by 2 minus of 5 into Y dash is minus 5 Y dash minus of 5 into 5 upon 2 is equal to minus of 25 by 2 plus 2 is equal to 0 which implies that X dash square plus Y dash square plus 9 upon 4 plus 25 by 4 minus of 9 by 2 minus of 25 by 2 plus 2 is equal to 0 on solving further we get X dash square plus Y dash square plus now taking the hc and we get 9 plus 25 minus 18 minus 50 plus 8 whole upon 4 is equal to 0 which is equal to X dash square plus Y dash square minus of 26 by 4 is equal to 0 which can also be written as X dash square plus Y dash square minus of 13 by 2 is equal to 0 and therefore it converts the equation from general form to the simplest form. This completes our session. Hope you enjoyed this session.