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Question 57061: is there any relation between ellipse parabola and hyperbola without showing figure how we can guess?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 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
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