I know that a general equation of the second degree represents a conic or a pair of straight lines. I evaluated the discriminant $\Delta$ which turns out to be equal to $ac-b^2$ which from the hypothesis is positive.
From this I concluded that the conic is an ellipse. However I've read that from any point, a maximum of four real normals can be drawn to an ellipse, yet the hypothesis states that five normals to the ellipse can be drawn from the origin. I've got no clue how to proceed.
Edit- To add to my confusion, the ellipse also is centred at origin with its axis inclined to the x,y axes. I simply don't see how there can be an odd number of normals from the centre to an ellipse to it as by symmetry I'd expect an even number of normals.