The two curves `x^3-3xy^2+2=0` and `3x^2y-y^3-2=0`

The two curves x^(3)-3xy^(2)+2=0 and 3x^(2)y-y^(3)-2=0

The two curves x^(3)-3xy^(2)+5=0 and 3x^(2)y-y^(3)-7=0

Find common tangent of the two curve y^(2)=4x and x^(2)+y^(2)-6x=0 (a) y=(x)/(3)+3 (b) y=((x)/(sqrt(3))-sqrt(3)) (c) y=(x)/(3)-3 (d) y=((x)/(sqrt(3))+sqrt(3))

The circumcentre of the triangle formed by the lines 2x^(2)-3xy-2y^(2)=0 and 3x-y=10 is

consider two curves ax^(2)+4xy+2y^(2)+x+y+5=0 and ax^(2)+6xy+5y^(2)+2x+3y+8=0 these two curves intersect at four cocyclic points then find out a