Prove that the equation m `(x^3-3xy^2)+y^3-3x^2y=0` represents three straight lines equally inclined to each other.

Prove that the equartion 3y^(2)-8xy-3x^(2)-29x+3y-18=0 represents two straight lines. Find also their point of intersection and the angle between them.

The equation 3ax^2+9xy+(a^2-2)y^2=0 represents two perpendicular straight lines for

Prove that the equation 8x^2+8xy+2y^2+26x+13y+15=0 represents a pair of parallel straight lines . Also find the perpendicular distance between them .

Prove that the equation (a+2h+b)x^2-2(a-b)xy+(a-2h+b)y^2=0 represents a pair of lines each inclined at an angle of 45^@ to one or other of the lines given by , ax^2+2hxy+by^2=0

Equation ax^3-9x^2y-xy^2+4y^3=0 represents three straight lines. If the two of the lines are perpendicular , then a is equal to

Prove that the equation 3x^(2) + 3y^(2) - 5x + 6y + 8 = 0 does not represent circle.

In R^(3) equation x^(2)+y^(2)=0 represents ____ .

The equation 3x^2+2hxy+3y^2=0 represents a pair of straight lines passing through the origin . The two lines are

For what value of lambda does the equation 12x^2-10xy+2y^2+11x-5y+lambda=0 represent a pair of straight lines ? Find their equations and the angle between them.

The equation ax^2+4xy+y^2+ax+3y+2=0 represents a parabola, then find the value of a.