[(111)x^(2)-2x-8],[(y)3x^(2)-x-4]

Prove that the curves y=x^(3)-3x^(2)-8x-4,y=3x^(2)+7x+4 touch each other and equation of the common tangent is x-y+1=0 .

The locus of a point "P" ,if the join of the points (2,3) and (-1,5) subtends right angle at "P" is x^(2)+y^(2)-x-8y+13=0 x^(2)-y^(2)-x+8y+3=0 x^(2)+y^(2)-4x-4y=0,(x,y)!=(0,4)&(4,0) x^(2)+y^(2)-x-8y+13=0,(x,y)!=(2,3)&(-1,5)

The equation of the circle passing through the point of intersection of the circles x^(2)+y^(2)-4x-2y=8 and x^(2)+y^(2)-2x-4y=8 and (-1,4) is (a)x^(2)+y^(2)+4x+4y-8=0(b)x^(2)+y^(2)-3x+4y+8=0(c)x^(2)+y^(2)+x+y=0(d)x^(2)+y^(2)-3x-3y-8=0

The number of second degree terms in the expression 2x^(3)-3x^(2)y+5x^(2)-6y^(2)+8x^(2)y-4x^(2)y^(2) is _____

Show that the following set of curves intersect orthogonally: y=x^(3) and 6y=7-x^(2)x^(3)-3xy^(2)=-2 and 3x^(2)y-y=2x^(2)+4y^(2)=8 and x^(2)-2y^(2)=4

The two circles x^(2)+y^(2)-2x-3=0 and x^(2)+y^(2)-4x-6y-8=0 are such that

The two circles x^(2)+y^(2)-2x-3=0 and x^(2)+y^(2)-4x-6y-8=0 are such that

Divide the given polynomial by the given monomial.( i (5x^(2)-6x)-:3x (ii) (3y^(8)-4y^(6)+5y^(4))-:y^(4)( iii) 8(x^(3)y^(2)z^(2)+x^(2)y^(3)z^(2)+x^(2)y^(2)z^(3))-:4x^(2)y^(2)z^(2)(iv)(x^(3)+2x^(2)+3x)-:2x(v)(p^(3)q^(6)-p^(6)q^(3))-:p^(3)q^(3)