Rotation Of Axes

We are given the equation , and we are asked to find the value of when the origin is shifted to .
Step 1: We first perform the translation of axes by substituting and , where and represent the new coordinates after translation. Substituting these into the given equation: Expanding the terms: Simplifying the equation: Rearranging the terms: Step 2: For the equation to not contain and the constant term, the coefficients of and the constant term must be zero. Therefore, we set the coefficient of to zero: Now, we set the constant term to zero: Substituting : Solving for : Step 3: Now, we can find the value of : Thus, the value of .