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Why is it wrong to use y for simultaneous elliptic equations?
The reason why y is used in elliptic equation is wrong: because there is no limit to the value range of y, the standard ellipse -a

The first formula gets y=(4x+k)/5, and then directly replaces y with the second formula. Y2+4Y- 1 = 0 has a negative solution. In fact, it should be noted that the vertical coordinates of these two intersections are equal, so it actually corresponds to a y value, which is a root of your unary quadratic equation, that is to say, at least one of y 1 and Y2 is greater than 0.

symmetrical

No matter whether the focus is on the X axis or the Y axis, the ellipse is always symmetrical about the X/Y/ origin.

When the focus is on the X axis, the vertices of the long axis are (-a, 0), (a, 0).

Vertex of minor axis: (0, b), (0, -b).

When the focus is on the Y axis, the vertices of the long axis are (0, -a), (0, a).

Vertex of minor axis: (b, 0), (-b, 0).

Pay attention to which axis the long and short axes represent respectively, which is easy to cause confusion here and needs to be understood step by step in combination with numbers and shapes.