If ax² + 2hxy + by² + 2gx + 2fy + c = 0, then show that

Given: ax² + 2hxy + by² + 2gx + 2fy + c = 0 …(i)

Differentiating the above with respect to x, we get

…(ii)

Now, we again differentiate eq (i) with respect to y, we get

…(iii)

Now, multiplying Eq. (ii) and (iii), we get

Hence Proved