How Do I Solve for the Intersection Points of Bounded Equations?

[ISU20CpreE]

I have to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated lines.

$$y=2x^2 , y=0 , x=2$$ It then wants me to figure out:

(a) the y-axis (b) the x-axis
(c) the line y=8 (d) the line x=2

In order to get the intersection points I need to equate the equations given to me. The problem is I really don't know how to equate the $$x=2$$
thats holding me to finish this problem. Please I need some advice.

 

[TD]

You mean you're only having trouble with question d? It's not really clear to me where you're stuck. What have you done so far?

 

[EnumaElish]

Not clear what the question is asking. You have a surface area on the XY plane bounded by two straight lines and a hyperbola. What does it revolving around to generate a solid?

 

[HallsofIvy]

You appear to be asking about the points of intersection of those three boundaries, but surely that's easy (If you are taking calculus).

The curves y= 2x², y= 0 intersect at y= 0= 2x² or x= 0, y= 0.
The curves y= 0, x= 2 intersect at (2,0), of course.
The curves y= 2x², x= 2 intersect at (2, 2(2)²)= (2,8).