# SOLUTION: byperbolas, last one i swear. first i would appreciate it if u defined some words for me and tell me what they are/do. Asymptote, transverse axis,what the a^2 and b^2 do. Next I

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: byperbolas, last one i swear. first i would appreciate it if u defined some words for me and tell me what they are/do. Asymptote, transverse axis,what the a^2 and b^2 do. Next I      Log On

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 Algebra: Conic sections - ellipse, parabola, hyperbola Solvers Lessons Answers archive Quiz In Depth

 Question 27833: byperbolas, last one i swear. first i would appreciate it if u defined some words for me and tell me what they are/do. Asymptote, transverse axis,what the a^2 and b^2 do. Next I dont get how to graph the hyperbolas, more specific how to pull info from the graph to the equation, whats standard form for a hyperbola. and last section my book gave me a formula xy=c is a hypebola with the x and y axis as asymptotes(dont know what it means) Sketch the graph of each hyperbola. they problem is xy=8 I promis I'll leave ya alone just lay some stuff out for me please!! thanks!Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!SEE FOLLOWING TO UNDERSTAND ASYMPTOTES AND THE AXES YOU WILL FIND 2 SYMMETRIC CURVES LYING HORIZONTALLY..THEY ARE A PAIR OF HYPERBOLAS .THEIR EQN.IS (X^2/9)-(Y^2/9)=1...THE GENERAL EQN. IS (X^2/A^2)-(Y^2/B^2)=1 THE OTHER PAIR OF HYPERBOLAS WHICH ARE IN A VERTICAL POSITION ARE CALLED CONJUGATE HYPERBOLAS OF THE EARLIER 2 HYPERBOLAS.THEIR EQN.IS (X^2/9)-(Y^2/9)= -1...THE GENERAL EQN. IS (X^2/A^2)-(Y^2/B^2)= -1 NOW WE DEFINE THE VARIOUS TERMS WITH RESPECT TO THE FIRST HYPERBOLAS GIVEN BY (X^2/9)-(Y^2/9)=1...THE GENERAL EQN. IS (X^2/A^2)-(Y^2/B^2)=1 DEFINITIONS....... HYPERBOLA IS THE LOCUS (OR PATH TRACED)BY A POINT WHICH MOVES SUCH THAT ITS DISTANCE FROM A FIXED POINT CALLED FOCUS TO ITS DISTANCE FROM A FIXED LINE CALLED DIRECTRIX IS CONSTANT (KNOWN AS ECCENTRICITY)AND IS MORE THAN 1. THERE ARE 2 FOCI AND 2 DIRECTIXES FOR THE HYPERBOLA GIVEN BY THE ABOVE DEFINITION AND EQN. X AXIS ALONG WHICH THE 2 HYPERBOLAS LIE IS CALLED TRANSVERSE AXIS.ITS EQN.IS Y=0 Y AXIS ALONG WHICH THE 2 CONJUGATE HYPERBOLAS ARE PRESENT IS CALLED THE CONJUGATE AXIS.ITS EQN.IS X=0 IF WE CALL THE 2 POINTS ON EITHER SIDE OF ORIGIN ON THE TRANSVERSE AXIS AT DISTANCE OF A FROM THE ORIGIN ARE NAMED A AND A' THEN AA'=2A IS THE LENGTH OF TRANVERSE AXIS IF WE CALL THE 2 POINTS ON EITHER SIDE OF ORIGIN ON THE CONJUGATE AXIS AT DISTANCE OF B FROM THE ORIGIN ARE NAMED B AND B' THEN BB'=2B IS THE LENGTH OF CONJUGATE AXIS ORIGIN IS THE CENTRE OF THE HYPERBOLAS ECCENTRICITY OF HYPERBOLA IS GIVEN BY E={(A^2+B^2)/(A^2)}^0.5 FOCI ARE GIVEN BY (A/E,0)AND(-A/E,0) EQNS.OF DIRECTRIX 1 AND 2 ARE GIVEN BY X=A/E AND X=-A/E. THE 2 LINES YOU FIND DIAGONALLY ALMOST RUNNING PARALLEL TO THE CURVES AT THEIR ENDS ARE CALLED ASYMPTOTES.THE CURVES APPROACH THESE LINES AS NEAR AS WE DESIRE AT AS FAR A DISTANCE AS NEEDED,BUT NEVER TOUCH THEM .THEY RUN PARALLEL AS THE CURVES AND THE LINES EXTEND TO INFINITY . **************************************************************************** GIVEN BELOW ARE SOME MORE EXAMPLES.NOW YOU TRY TO DRAW YOUR REQUIRED CURVE AND UNDERSTAND.IF STILL IN DIFFICULTY COME BACK. ****************************************************************************** Find the equations of the vertical and horizontal asymptotes for the graph of the rational function whose equation is f(x) = x/x+3. LET Y =X/(X+3)..D.R IS ZERO AT X=-3..SO THIS IS A CRITICAL POINT WHERE THE FUNCTION IS NOT DEFINED. HENCE WE SPLIT THE DOMAIN OF X 1. FROM -INFINITY TO LESSTHAN -3 2. AND GREATER THAN -3 TO +INFINITY THE GRAPH FOR DOMAIN 1. FROM -INFINITY TO LESSTHAN -3 IS AS FOLLOWS. ALGEBRAICALLY , WE FIND THE RANGE OF Y VARIES FROM 1 TO INFINITY. SO ASYMPTOTES ARE Y=1 AS X TENDS TO MINUS INFINITY AND Y TENDING TO INFINITY AS X APPROACHES -3 THE GRAPH FOR DOMAIN 2. FROM GREATER THAN -3 TO +INFINITY IS AS FOLLOW ALGEBRAICALLY , WE FIND THE RANGE OF Y VARIES FROM MINUS INFINITY TO 1. SO ASYMPTOTES ARE Y=1 AS X TENDS TO INFINITY AND Y TENDING TO MINUS INFINITY AS X APPROACHES -3