the equation of the common tangent to the curves y2=8x and xy=-1 is y=x+2

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Please find below the solution to the asked query:

y2=8xy2=42xWe know that equation of tangent of slope 'm' isy=mx+amy=mx+2mThis tangent also touches xy=-1Hence put y=mx+2mxmx+2m=-1mx2+2xm=-1mx2+2x+m=0As tangent touches curve at one point, hence disciminant is 022-4×m×m=04m2=4m2=1m=1y=mx+2my=x+2

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