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Take points A(7/2,0), B(0,7) and C(-7/6,0) on the xy-plane. The parabola y=-x^2+ax+b is tagent to both lines BA and BC.
\n" ); document.write( "1) Determine a and b
\n" ); document.write( "2) Calculate the area of the domain bounded by the line BA, the parabola and the y-axis.
\n" ); document.write( "SLOPE OF AB = (7-0)/(0-7/2)= -2
\n" ); document.write( "SLOPE OF BC = (7-0)/(0+7/6)=6
\n" ); document.write( "BA AND BC ARE TANGENTS THROUGH A COMMON POINT B.HENCE EQN.OF CHORD OF CONTACT OF B(0,7) IS
\n" ); document.write( "(Y+7)/2= -X*0+A(X+0)/2+B
\n" ); document.write( "Y+7=AX+2B OR ..Y=AX+2B-7 .I
\n" ); document.write( "THIS MEETS PARBOLA .Y= -X^2+AX+B ... AT
\n" ); document.write( "AX+2B-7= -X^2+AX+B
\n" ); document.write( "X^2=7-B .OR X=+(7-B)^0.5 AND -(7-B)^0.5
\n" ); document.write( "FOR X=(7-B)^0.5 ..Y=A(7-B)^0.5+2B-7 .LET THIS BE POINT P ON THE CURVE.
\n" ); document.write( "FOR .X= -(7-B)^0.5 Y= -A(7-B)^0.5+2B-7 ..LET THIS BE POINT Q ON THE CURVE.
\n" ); document.write( "SLOPE OF BAP = -2 ={A(7-B)^0.5+2B-7-7}/{(7-B)^0.5-0}
\n" ); document.write( "-2(7-B)^0.5=A(7-B)^0.5+2B-14 ..OR (A+2)(7-B)^0.5+2B-14=0 ..II
\n" ); document.write( "SLOPE OF BCQ =6={-A(7-B)^0.5+2B-7-7}/{-(7-B)^0.5-0}
\n" ); document.write( "-6(7-B)0.5=-A(7-B)^0.5+2B-14 ..OR (6-A)(7-B)^0.5+2B-14=0 ..III
\n" ); document.write( "EQN.II - EQN.III GIVES
\n" ); document.write( "(2A-4)(7-B)^0.5=0 .2A=4 ..OR A=2
\n" ); document.write( "SUBSTITUTING IN EQN.II WE GET
\n" ); document.write( "4(7-B)^0.5=2(7-B)
\n" ); document.write( "2=(7-B)/(7-B)^0.5=(7-B)^0.5
\n" ); document.write( "7-B=4 OR B=3 .HENCE EQN. OF CURVE IS Y= -X^2+2X+3=4-(X-1)^2
\n" ); document.write( "-------------------------------------------------------------------------------
\n" ); document.write( "EQN. OF BA IS Y-7= -2(X-0)......Y=7-2X
\n" ); document.write( "HOPE YOU KNOW INTEGRATION .THE SECOND BIT NEEDS INTEGRATION.FIRST SEE THE GRAPH
\n" ); document.write( "
\n" ); document.write( "THE QUESTION IS AREA OF DOMAIN BOUNDED BY Y AXIS WHOSE EQN. IS X=0....
\n" ); document.write( "BA LINE WHOSE EQN.IS....Y=7-2X......AND PARABOLA WHOSE EQN.IS..Y=4-(X-1)^2..
\n" ); document.write( "THIS IS NOT VERY CLEAR...YOU CAN SEE ROM GRAPH...THIS IS OPEN TO DIFERENT INTERPRETATIONS.IF IT IS MADE CLEAR WE CAN DO IT USING INTEGRATION...
\n" ); document.write( "FOR EX. THE QUESTION COULD BE AREA BETWEEN Y AXIS,BA LINE AND THE CURVE UPTO TANGENT POINT P AS WE CALLED IT.P IS (2,3)....
\n" ); document.write( "BELOW THIS TANGENT POINT WHAT DOES THE DOMAIN BETWEEN BA,Y AXIS AND PARBOLA HAS NO MEANING..EITHER WE CAN HAVE DOMAIN BETWEEN BA AND PARABOLA ...OR...BETWEEN BA AND Y AXIS ...OR BETWEEN Y AXIS AND PARABOLA.SO PLEASE CHEKUP AND COME BACK TO KNOW THE SOLUTION.ALSO CONFIRM YOU KNOW INTEGRATION. \n" ); document.write( "