Question

the conic is called pair of straight line if ?​

Answer 1

If a cone is cut by a plane through the vertex, the section is a triangle." (Apollonius, Conics, I, 3). Ignore the base of the triangle, which is a straight line within the circular base of the cone, and you have the two intersecting straight lines on the conic surface. That's a pair of lines in the y=0 plane.