Prove that `a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0` represents a straight line parallel to the y-axis.

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 .

Number of straight lines represented by x^5+y^5 = 0 is ……

If the equation 2x^(2)+2hxy +6y^(2) - 4x +5y -6 = 0 represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal to

If the equation 3x^(2)+xy-y^(2)-3x+6y+k=0 represents a pair of straight lines, then the value of k, is

Locus of the image of the point (2, 3) in the line (2x-3y""+""4)""+""k""(x-2y""+""3)""=""0,""kepsiR , is a : (1) straight line parallel to x-axis. (2) straight line parallel to y-axis (3) circle of radius sqrt(2) (4) circle of radius sqrt(3)

The value of lambda for which the equation x^2-y^2 - x - lambda y - 2 = 0 represent a pair of straight line, are

The equation x^(3)+x^(2)y-xy^(2)-y^(3)=0 represents three straight lines passing through the origin such that

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mu .

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mu .

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mudot