Question

The point to which origin is shifted in order to miss tge first degree terms in 2x square +5xy+3y square +6x+7y+1=0 is​

Answer 1

Transformation of co-ordinates

• To find. the point to which the origin is to be shifted in order to miss the first degree terms in 2x² + 5xy + 3y² + 6x + 7y + 1 = 0

Solution. Let the point to which the origin is to be shifted be (p, q).

Substituting x = x' + p, y = y' + q, the given equation becomes

2 (x' + p)² + 5 (x' + p) (y' + q) + 3 (y' + q)² + 6 (x' + p) + 7 (y' + q) + 1 = 0

The coefficients of x' and y' in the transformed equation are

(4p + 5q + 6) and (5p + 6q + 7),

which will be separately zero, if the first degree terms are to be removed.

Thus 4p + 5q + 6 = 0 and 5p + 6q + 7 = 0

Solving we get: p = 1, q = - 2.

Answer. Hence the origin must be shifted to the point (1, - 2).