The intersection point between a paraboloid and a normal line is where the normal line is tangent to the paraboloid. This point is also known as the point of tangency.
To find the normal line to a paraboloid, you first need to find the gradient of the paraboloid at the point of intersection. Then, you can use this gradient to find the equation of the normal line using the point-slope formula.
No, a paraboloid can only intersect a normal line at one point. This is because a normal line is always perpendicular to the tangent line of a curve, and a paraboloid only has one tangent line at any given point.
The intersection of a paraboloid and a normal line is significant because it represents the point where the normal line is tangent to the paraboloid. This point is important in understanding the shape and behavior of the paraboloid at that particular point.
No, a normal line cannot be parallel to a paraboloid. This is because a normal line is always perpendicular to the tangent line of a curve, and a paraboloid only has one tangent line at any given point. If the normal line were parallel to the paraboloid, it would not intersect with it.