Symmetry 3
Question
Use algebraic tests to determine whether the graph of the equation 4x² – 9y² = 1 is symmetric with respect to the x-axis, y-axis, or origin
Answer
Now a little definition first.
A point ( x,y ) is said to be symmetric with respect to the :
1) x -Axis if the point (x, -y) still lies on that curve.
2) y -Axis if the point (-x, y) still lies on that curve.
3) The origin (0,0) if the point (-x, -y) still lies on that curve.
So we just need to ‘check’ the conditions (1), (2) & (3) above for the equation given for our curve.
To check for (1), consider
4(x)² – 9(-y)² = 4x² – 9y² = 1; and thus this point lies on the curve since it satisfies the equation!
Similarly, for ( 2 ),
4(-x)² – 9(y)² = 4x² – 9y² = 1; and thus this point lies on the curve since it satisfies the equation!
For (3),
4(-x)² – 9(-y)² = 4x² – 9y² = 1; and thus this point lies on the curve since it satisfies the equation!
Thus we have shown that our graph for the curve 4x² – 9y² = 1 is symmetrical for all three x – axis, y – axis and the origin!
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