Q12 Conic Sections (HARD)

Note the equation of the plane is z = some constant.  Change the equation of this yellow plane to z = 2.  Then change it to z = 1. Then change it to z = 4.    1.How would you describe the intersection of this plane and double-napped cone?   

2.Change the equation of the plane to z=x+2  .  How would you describe the intersection of this plane and double-napped cone now?  And find the equation of the intersecting curve.

3.Change the equation of the plane to z=0.5x+2 .  How would you describe the intersection of this plane and double-napped cone now?  And find the equation of the intersecting curve.

4.Change the equation of the plane to z=4x+2 .  How would you describe the intersection of this plane and double-napped cone now?  And find the equation of the intersecting curve.