x^2+2hxy+by^2+2gx+2fy+c=0, depends upon a, b,c,h,g,f

Summary With the help of this activity, we have learnt that: When a=b and h=0 then the conic section ax^2+2hxy+by^2+2gx+2fy+c=0 will be a circle and vice versa. When h^2=ab then the conic section ax^2+2hxy+by^2+2gx+2fy+c=0 will be a parabola and vice versa. When h^2<ab then the conic section ax^2+2hxy+by^2+2gx+2fy+c=0 will be an ellipse and vice versa. When h^2>ab then the conic ax^2+2hxy+by^2+2gx+2fy+c=0 will be a hyperbola and vice versa. When abc + 2fgh – af2 – bg2 – ch2 = 0 then the conic section ax^2+2hxy+by^2+2gx+2fy+c=0 will become a pair of straight lines and vice versa.

 

Mathguru

 
Resource Type
Activity
Tags
x^2+2hxy+by^2+2gx+2fy+c=0 
Target Group (Age)
19+
Language
English (United Kingdom)
 
 
GeoGebra version
4.0
Views
1823
Report a problem
 
 
© 2018 International GeoGebra Institute