Question

Algebraically determine if the relation x = y2 – 100 is symmetrical with respect to the x-axis, y-axis, or the origin.

Answer 1

Answer: Option D: x-axis symmetry

Step-by-step explanation:

The symmetry concept can be explained as below:

1. If any point say, (x,y) on the graph, then (x,-y) is also on the graph, it shows x- axis symmetry.
2. If any point say, (x,y) lies on the graph, then, (-x,y) should also lie on the same graph, then is shows y-axis symmetry.  

Now, here the graph is for x = y^{2}-100  is attached.

Suppose, (x,y) = (-100,0)

then, solving this point satisfies the equation of given graph.

Also, (x,-y) = (-100,0) satisfies the equation of the given graph.

Hence, the relation x = y^2 – 100 is symmetrical to x-axis.