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Find dy/dx if ax^2+2hxy+by^2+2gx+2fy+c=0...

Find `dy/dx if ax^2+2hxy+by^2+2gx+2fy+c=0`

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Given `ax^(2) + by^(2) + 2hxy + 2gx + 2fy + c=0`
Differentiating both sides w.r.t x, we get
`a d/(dx)x^(2) + 2hd/(dx) (xy) +bd/(dx)y^(2) + 2g d/(dx) (x) +2f d/(dx) (y) + 0=0`
` 2ax + 2h (x(dy)/(dx) + y.1) + 2by (dy)/(dx) + 2g + 2f (dy)/(dx) =0`
` (2ax +2hy +2g) + (dy)/(dx) (2hx +2by +2f) =0`
` (dy)/(dx) = - (ax +hy+g)/(hx +by +f)`
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