.True of False
The trace of x^2+2y^2 +10z^2=5 in the plane z=2 is an ellipse.
False because x^2+2y^2=-35 is an ellipse, so true is that correct?
Please do read the last line you wrote above and tell me if you really expect anyone but yourself to understand it: what are you asking there?? Is like the following:
Claim: A is B
Answer: False because A is B, so true is that correct?
Does this make any sense to you?
Btw, the answer is, of course, false, since sum of squares and positives cannot be a negative number