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Mathematica works well with many kind of plots, but I cant figure out how to plot conic sections with rotated axis. For example "plot $y = (3x + \sqrt{x(16-7x)})/4, y = (3x - \sqrt{x(16-7x)})/4$" will not give me an ellipse, but gives me a zigzag mix of real and imaginary parts lines. How do I get rotated conic? Can you provide examples of hyperbola and parabola also?

Here a stub to meet demands of code formatting

Plot[y /. Solve[y == (3 x + sqrt (x (16 - 7 x)))/4], {x, -20, 20}]
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    $\begingroup$ Your code isn't useable as is, try to copy it directly from your notebook (I assume you would see the error with sqrt instead of Sqrt). Also, your Solve isn't formatted correctly, you already have it solved for y. $\endgroup$ – Jason B. Jan 28 '16 at 11:00
  • $\begingroup$ I recommend to play around with parametric representations of conic sections $\endgroup$ – Artes Jan 28 '16 at 11:08
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Your ellipse plots pretty easily if you get the syntax right.

Plot[{(3 x + Sqrt[x (16 - 7 x)])/4, (3 x - Sqrt[x (16 - 7 x)])/4}, {x, 0, 2.5}]

plot

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