Need help with rendering algorithm in C++

I need help with implementing a raytracer to render spheres and planes with different projections in C++.

You will be a good fit if you are familiar with some of the below topics:
3D Transformations
Viewing 3D scenes
Shading
Rendering pipeline and the GPU
Texturing
Polygonal meshes and other modelling techniques
Colour spaces
Light and colour
Ray-geometry intersection
Ray tracing