(CIE 0606/2021/m/22/Q4)
The curve 4x2+54y2=1 and the line x+2y=0 intersect at two points. Find the exact distance between these points. [6]
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(CIE 0606/2021/m/22/Q4)
The curve 4x2+54y2=1 and the line x+2y=0 intersect at two points. Find the exact distance between these points. [6]
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*********math solution************* x+2y=0⇒x=−2y⇒x2=(−2y)2=4y2 Thus 4x2+5x2=19x2=1x2=9x=±3 when x=3,y=−x2=−32. Thus intersection point P=(3,−32) when x=−3,y=−x2=32. Thus intersection point Q=(−3,32)PQ=√(−3−3)2+(32−(−32))2=√36+9=√45=3√5.
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