What does the equation y = x^2 represent as a curve in IR^2? What does it represent as a surface in IR^3? What does the equation z = y^2 represent?

## Answer

**(a)**we are given y=x^2 on R^2 R^2 means two dimensional it is xy-plane we know that y=x^2 is equation of parabola

**Hence , parabola is answer**

**(b)**we know that when we plot y=x^2 the value of ‘y’ aned ‘x’ will vary .. but ‘z’ can be any value Hence , graph will look like parabolic cylinder

**Hence , parabolic cylinder is answer**

**(C)**we know that when we plot z=y^2 the value of ‘z’ aned ‘y’ will vary .. but ‘x’ can be any value Hence , graph will look like parabolic cylinder

**Hence , parabolic cylinder is answer**