Discreteness of Electron Orbits: Elliptical Shapes?

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We know that orientations of electron orbit are discrete , what exactly do you mean by discreteness ,& also is there any particular shape of orbits like an ellipse ?
 
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For a classical orbit, "discreteness" means that the plane of the orbit can only be oriented in certain directions but not in others. For a quantum-mechanical orbital, the electron doesn't move in a definite path like a satellite going around the Earth (so you can't talk about circles and ellipses), but you can still talk about the angular momentum vector being constrained to certain magnitudes and directions.