-160,25 are the coordinates
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The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².
<h3>How to derive the equation of the parabola from the locations of the vertex and focus</h3>
Herein we have the case of a parabola whose axis of symmetry is parallel to the x-axis. The <em>standard</em> form of the equation of this parabola is shown below:
(x - h) = [1 / (4 · p)] · (y - k)² (1)
Where:
- (h, k) - Coordinates of the vertex.
- p - Distance from the vertex to the focus.
The distance from the vertex to the focus is 1 / 8. If we know that the location of the vertex is (0, 0), then the <em>standard</em> form of the equation of the parabola is:
x = 2 · y² (1)
The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².
To learn more on parabolae: brainly.com/question/4074088
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The "system" of equations can't be solved for (x, y), because there's no "system" of equations given. There's really only one equation.
Either of these two equations can be massaged to look exactly like the other one. And if you graph both equations, you find that they're both the same line on the graph.
ANY point on the line is a solution to both equations ... and we all know how many different points there are on a line.