Question

Which of the following equations represents an elliptic paraboloid ?

 

 

1. $z=y^2$
2. $z=x^2-y^2+2y$
3. $z=x^2+y^2+2x$
4. $z=x^2-y^2+2x$

Answer 1

The equation of an elliptic paraboloid:

$z=Ax^2+By^2$

where A and B have the same sign.

Answer: $z=x^2+y^2+2x$

or $z+1=(x+1)^2+y^2$