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The graph of 2y^4 -x^2 +11 =0 is symmetric with respect which of the following?
1. The x axis
2. The y axis
3. The origin
A) only 1
B) only 2
C) only 3
D) 1, 2, and 3
Plot y1 = (red) and y2 = (green).
The correct answer is OPTION D).
0. Let the point (x,y) belongs to the curve.
It means that its coordinates satisfy the equation
2y^4 -x^2 +11 =0. (1)
1. Then the point (-x,y) also belongs to the curve.
Indeed, then 2y^4 - (-x)^2 + 11 = 2y^4 - x^2 + 11 = 0 due to (1).
It means that the symmetry (x,y) --> (-x,y) relative to the axis "Y" is in place.
2. Also, then the point (x,-y) belongs to the curve.
Indeed, then 2(-y)^4 - x^2 + 11 = 2y^4 - x^2 + 11 = 0 due to (1).
It means that the symmetry (x,y) --> (x,-y) relative to the axis "X" is in place.
3. Finally, then the point (-x,-y) belongs to the curve.
Indeed, then 2(-y)^4 - (-x)^2 + 11 = 2y^4 - x^2 + 11 = 0 due to (1).
It means that the symmetry (x,y) --> (-x,-y) relative to the origin is in place.
Thus my statement is PROVED and the solution is COMPLETED.
Proved. Solved. And completed.
The other's tutor solution is WRONG (his approach is WRONG and his answer is UNCOMPLETED).