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`        From where does this equation: h^2-ab comes in conic sections and what does it represents?`
one year ago

```							  The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0. Represents a second degree equation where a, h, b doesn’t variables simultaneously. Let a ≠ 0. Now, the above equation becomes         a2 x2 + 2ax (hy + g) = aby2 – 2afy – ac on completing the square on the left side, we get,         a2 x2 + 2ax (hy + g) = y2 (h2 – ab) + 2y (gh – af) + g2 – ac. i.e.    (ax + hy + g) = + √y2(h2–ab)+2y(gh–af) +(g2–ac) We cannot obtain x in terms of y, involving only terms of the first degree, unless the quantity under the radical sign be a perfect square. The condition for this is, (gh – af)2 = (h2 – ab) (g2 – ac) hope it clears. Now if Delta is 0 	h^2 – ab > 0 intersecting real lines	h^2 – ab = 0. parallel lines	h^2 – ab
```
one year ago
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