What is the condition for a conic x2+2xy+2y+kx+3y2=0 to represent a pair of straight lines.
This is a straight forward condition. For a conic of the general form,
ax2+2hxy+2gx+2fy+by2+c=0 to represent a pair of straight line, the required condition in determinant form is,
∣∣ ∣∣ahghbfgfc∣∣ ∣∣=0
The given conic equation is,
Putting these values in the condition we get,
∣∣ ∣ ∣∣11k2111k211∣∣ ∣ ∣∣=0
∣∣ ∣ ∣∣11k2−1111k211∣∣ ∣ ∣∣=0
Which is the required condition.