# Paraboloid and Cylinder surface

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Answered: Vimal Rathod on 23 Jun 2021
We know that x^2+y^2=4*f*z, where f is the focal length of the paraboloid. Given that the cylinder (x-a)^2+y^2<=r^2, where a is the distance between the axis of the cylinder and the axis of the paraboloid.r is the radius of the cylinder. The surface on the paraboloid intercepted by the cylinder is obtained by using the above equation. Question: How to input f, a and r to obtain the image of intersecting surface and extract the coordinates of N points from the surface?

Vimal Rathod on 23 Jun 2021
Hi,
From the given equations in your question the solution to the value would be (0,0) as the equation of cylinder creates a surface on z = 0 and the equation of paraboloid creates a paraboloid with only one point of intersection with the cylinderical surface.
Suppose you want to solve a set of equations, you could use the following link to solve the given set of equations.
You could refer to the following link to know more about how to create equations in matlab

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