COORDINATE GEOMETRY | LOCUS AND EQUATION OF A LOCUS, POLAR COORDINATES, SHIFTING OF ORIGIN, ROTATION OF AXIS | What is locus and equation of the locus of point ?, Condition when variable is not involved (i)The sum of the square of the distances of a moving point from two fixed point `(a;0) and (-a;0)` is equal to the constant quantity `2c^2`. Find the equation to its locus ?, Condition when variable is involved :(ii) Find the locus of point of intersection of the lines `xcosalpha+ysinalpha=a` and `xsinalpha-ycos alpha=b` where b is the variable., What is polar coordinates ? Explain with the help of diagram., Conversion of coordinates in Polar conversion form:(i) Convert the following Cartesian coordinates to the corresponding polar coordinates using positive r and negative r . (i)(-1;1) (ii) (2;-3), Explanation of determining new coordinates of the point or new locus: At what point should the origin be shifted if the coordinates of a point (4;5) become (-3;9)?, What is the Formula Derivation to find new coordinates when axes are rotated?, Formula derivation by complex numbers, Why we need rotation for Removal of term `xy` from `F(x, y) = ax^2 + 2 h xy + b y^2`, How the equation is transformed when origin is changed and axes is rotated ?