minimum number of points needed to define a unique 2 degree curve

Question

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

Answer 1

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