Question

The point to which the
origin is to be shifted by
the translation of axes
so as to remove the first
degree terms from the
equation ax2 + 2hxy +
by2 + 2gx + 2fy + c = 0 is​

Answer 1

Answer:

Suppose that the origin is shifted to the point (x1, y1) and let x = X + x1, y = Y + y1 . Therefore, the given equation is transformed to a(X + x1)2 + 2h (X + x1) (Y + y1) + b(Y + y1)2 + 2g (X + x1) + 2f Y + y1 + c = 0 Therefore, the origin is to be shifted to the point (hf - bg/ab - h2 , gh - af/ab - h2) so so that Eq. (1.5) will be aX2 + 2hXY + bY2 + gx1 + fy1 + c = 0 Where x1 and y1 are as defined above.Read more on Sarthaks.com - https://www.sarthaks.com/494357/then-remove-the-first-degree-terms-the-equation-2hxy-2gx-the-origin-be-shifted-to-the-point