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Coordinate Geometry (Intersect points)

(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=0x=2yx2=(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=(33)2+(32(32))2=36+9=45=35.
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