I am building a ray Tracer from scratch. My question is: When I change camera coordinates the Sphere changes to ellipse. I don't understand why it's happening. Here are some images to show the artefacts:
Sphere: 1 1 -1 1.0 (Center, radius)
Camera: 0 0 5 0 0 0 0 1 0 45.0 1.0 (eyepos, lookat, up, foy, aspect)

But when I changed camera coordinate, the sphere looks distorted as shown below:
Camera: -2 -2 2 0 0 0 0 1 0 45.0 1.0

I don't understand what is wrong. If someone can help that would be great!
I set my imagePlane as follows:

//Computing u,v,w axes coordinates of Camera as follows: 
{ 
Vecter a = Normalize(eye - lookat); //Camera_eye - Camera_lookAt 
Vecter b = up; //Camera Up 
Vecter m_w = a;
Vecter m_u = b.cross(m_w); 
m_u.normalize(); 
Vecter m_v = m_w.cross(m_u); 
}

After that I compute directions for each pixel from the Camera position (eye) as mentioned below:

//Then Computing direction as follows: 
int half_w = m_width * 0.5; 
int half_h = m_height * 0.5; 
double half_fy = fovy() * 0.5; 
double angle = tan( ( M_PI * half_fy) / (double)180.0 ); 

for(int k=0; k<pixels.size(); k++){ 
  double j = pixels[k].x(); //width 
  double i = pixels[k].y(); //height

 double XX = aspect() * angle * ( (j - half_w ) / (double)half_w ); 
 double YY = angle * ( (half_h - i ) / (double)half_h ); 

 Vecter dir = (m_u * XX + m_v * YY) - m_w ; directions.push_back(dir); 
}

After that:

for each dir: 
Ray ray(eye, dir); 
int depth = 0; 
t_color += Trace(g_primitive, ray, depth);

I have only provided the code which I think is important. But if more code snippets are required then I will provide those.

Thanks for your help.