Precalculus

The light pattern from a fog light at the airport can be modeled by the equation x^2/4 - y^2/16=1. One of the points on the graph is at (3, 4.5) and one of the x-intercepts is -2. Find the coordinates of the three addditional points on the graph and the other x-intercept.

I'm pretty sure I have to check the line symmetry of the x and y-axis and the lines y=x and y=-x. But as for getting the other x-intercept, I have no idea what to do at all. Thanks in advance.

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  1. To get the x intercept for any equation let y=0 and solve.
    You should recognize your equation to be that of a standard hyperbola, with symmetrical x and y intercepts.
    so the other x intercept would be x=-2

    the other 3 points would be (3,-4.5), (-3,4.5) and (-3,-4.5)

    BTW, the y value is approximately 4.5, actually it would be √20

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