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What is the equation of conics whose axes coincide with axis of coordinates

What is the equation of conics whose axes coincide with axis of coordinates

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
The general equation of all such conics would be, ax^2+cy^2=bx+dy+f . 
If a, c, f are positive and a=c and b=d=0 , then it represents a circle.
If , a, c, f are positive, a is not equal to c and b=d=0, then it represents an ellipse.
If either of a or c is negative, f is positive and b=d=0, then it represents a hyperbola.
If, a=d=0 or b=c=0 and remaining constants are are positive numbers, then it represents a parabola.
It is to be noted that axes of all of the above figures will coincides with one of the either of the coordinate axes.
 
 
Regards
Arun (askIITians forum expert)

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