a traingle has the lines y=m1x and y=m2 x for two of its sides,where m1 and m2 are the roots of the equation x2+ax-1=0,then find the orthocentre of triangle

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Please find below the solution to the asked query:

We havey=m1x and y=m2xm1 and m2 are roots of x2+ax-1=0Product of roots=m1m2=-1which means y=m1x and y=m2x are perpendicular to each otherHence orthocentre will be at their point of intersection.And point of intersection of  y=m1x and y=m2x is 0,0Hence orthocentre is 0,0

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