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as the title says to find minimum number of points needed to define a unique 2 degree. i did it by thinking that in general equation of 2 degree $Ax^2 + By^2 + 2Gx + 2Fy + 2Hxy + C $ there are 6 variables and there so minimum 6 points are needed to define a 2 degree curve. is my approach correct ? if not please tell how to solve this problem. thanks

Neelesh Vij
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  • If it is a circle you need only 3 points, so the minimum must be equal or smaller than 3 –  Oct 14 '15 at 16:10

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In general case, you need 5 points to determine a conic . The minimum is 3 points, circle case. Not much to prove here considering there are three types of conics 1. Parabola 2. Circle and ellipse 3. Hyperbola

  • is there any prove to it? – Neelesh Vij Oct 14 '15 at 17:15
  • There are 6 variables in the formula but they are not all independent .If you double each of them the formula still totals zero. If H=0 the formula can be re-arranged (complete the squares) to yield a standard form for a conic section or a "degenerate conic section" (2 lines,1 line,1 point,or the empty set).If H is not 0, you change x,y to the co-ordinates u,v with respect to a different pair of orthogonal axes ,to get a quadratic form in u,v for which the co-efficient of uv is zero. – DanielWainfleet Oct 14 '15 at 18:37