Question 57061
is there any relation between ellipse parabola and hyperbola without showing figure how we can guess?
I AM GIVING SOME INDICATIVE TESTS FOR SIMPLE CASES INVOLVING STANDARD 
EQUATIONS WHICH WILL SERVE FOR MOST OF YOUR  PRELIMINARY PURPOSES.
I START PREPARATION.
1.THEY SHOULD BE ALL SECOND DEGREE EQUATIONS IN X AND Y
 AND THERE ARE NO TERMS INVOLVING XY.
2.COMBINE ALL X TERMS TO FORM A PERFECT SQUARE.
3.COMBINE ALL Y TERMS TO FORM A PERFECT SQUARE.
4.TAKE ALL CONSTANT TERMS ON RIGHT SIDE KEEPING X AND Y 
  TERMS ON LEFT SIDE
II.INDICATIONS
PARABOLA:
1.THERE ARE ONLY X TERMS FORMING A PERFECT SQUARE AND Y TERMS ARE
 IN FIRST DEGREE.......OR......
 THERE ARE ONLY Y TERMS FORMING A PERFECT SQUARE AND X TERMS ARE 
 IN FIRST DEGREE.
  THEN IT IS LIKELY TO BE A PARABOLA.
ELLIPSE :
1. X TERMS FORMING PERFECT SQUARE AND Y TERMS FORMING PERFECT SQUARE 
   ON LEFT SIDE ARE SEPERATED BY A +VE(PLUS) SIGN.
   THEN IT IS LIKELY TO BE AN ELLIPSE  
HYPERBOLA :
1. X TERMS FORMING PERFECT SQUARE AND Y TERMS FORMING PERFECT SQUARE 
   ON LEFT SIDE ARE SEPERATED BY A - VE(MINUS) SIGN.
   THEN IT IS LIKELY TO BE A HYPERBOLA