In a three-dimensional `x y z` space , the equation `x^2-5x+6=0` represents a. Points b. planes c. curves d. pair of straight lines

x^2-x y+y^2-4x-4y+16=0 represents a. a point b. a circle c. a pair of straight line d. none of these

The equation x^2y^2-9y^2-6x^2y+54 y=0 represents (a) a pair of straight lines and a circle (b) a pair of straight lines and a parabola (c) a set of four straight lines forming a square (d) none of these

The equation 3x^2+4y^2-18x+16 y+43=k (a)represents an empty set, if k 0 (c)represents a point, if k=0 (d)cannot represent a real pair of straight lines for any value of k

Prove that the equation 2x^2+5x y+3y^2+6x+7y+4=0 represents a pair of straight lines. Find the coordinates of their point of intersection and also the angle between them.

If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight line c. a pair of straight line d. none of these

The value of lambda with |lambda| lt 16 such that 2x^(2) - 10xy +12y^(2) +5x +lambda y - 3 = 0 represents a pair of straight lines is

Find the value of k, if the following equation represents a pair of straight lines . Further find wheter these lines are parallel or intersecting 12x^(2) + 7xy - 12 y^(2) - x + 7y + k = 0

Does equation x^2+2y^2-2sqrt(3)x-4y+5=0 satisfies the condition a b c+2gh-af^2-bg^2-c h^2=0? Does it represent a pair of straight lines?

Find the value of k if the following equation represents a pair of straight lines. Further, find whether these lines are parallel or intersecting 12x^(2)+7xy-12y^(2)-x+7y+k=0 .