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ASYMPTOTES ARE
\n" ); document.write( "Y=2X OR .Y-2X=0 I ..AND
\n" ); document.write( "Y=-2X OR .Y+2X=0 II ...SO THEIR COMBINED EQN.IS GIVEN BY EQN.I*EQN.II=0
\n" ); document.write( "(Y-2X)(Y+2X)=0=Y^2-4X^2=0 EQN.3.
\n" ); document.write( "IT IS KNOWN THAT THE EQN.OF HYPERBOLA DIFFERS FROM THE COMBINED EQN.OF ASYMPTOTES ONLY BY A CONSTANT.
\n" ); document.write( "SO EQN.OF HYPERBOLA IS .
\n" ); document.write( "Y^2-4X^2=C ..III ...WHERE C IS A ONSTANT TO BE FOUND PUTTING THIS EQN.IN STD.FORM WE GET
\n" ); document.write( "Y^2/C -4X^2/C =1 .OR ..
\n" ); document.write( "(Y-0)^2/C - (x-0)^2/(C/4) =1 IV
\n" ); document.write( "COMPARING WITH STANDARD EQN.OF HYPERBOLA
\n" ); document.write( "(Y-K)^2/B^2-(X-H)^2/A^2=1. V
\n" ); document.write( "WHERE VERTICES ARE...(H,(K-B)) AND (H,(K+B)) GIVEN HERE AS (0,-5) AND (0,5)
\n" ); document.write( "WE GET H=0
\n" ); document.write( "K+B=5
\n" ); document.write( "K-B=-5
\n" ); document.write( "ADDING THE ABOVE 2 EQNS ..2K=0 OR K=0
\n" ); document.write( "SO B=5
\n" ); document.write( "COMPARING EQN.IV,WITH STD.EQN.V,WE GET .
\n" ); document.write( "H=0 ..K=0 .C=B^2 ..C/4=A^2 .BUT B=5 WE FOUND .SO
\n" ); document.write( "C=5^2=25 .A^2=25/4
\n" ); document.write( "HENCE EQN.OF HYPERBOLA IS AS PER EQN.III IS
\n" ); document.write( "Y^2-4X^2=25 \n" ); document.write( "