Number of common points on two parabolas (perpendicular to the axis)
Author: shiroeExecutions: 32
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Enter a, b, c, l, m, and n.
Enter non-zero values for a and l (no output will be generated if 0 is entered).
Output the number of common points.
Output the coordinates of the common points.
Enter non-zero values for a and l (no output will be generated if 0 is entered).
Output the number of common points.
Output the coordinates of the common points.
| Number of common points | |
| x1 | y1 |
| x2 | y2 |
Digit display setting: 50 digits. Can be changed. Real number calculation mode.
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Consider the xy-plane (the real plane with the y-axis as the vertical axis and the x-axis as the horizontal axis).
Let the equation of Parabola 1 be y = ax² + bx + c.
Let the equation of Parabola 2 be y = lx² + mx + n.
Both axes are vertical.
Coefficients and constant terms are real numbers.
If there are common points, calculate their x- and y-coordinates.
If there is one common point, output it to the output fields x1 and y1.
If there are two common points, also output them to the output fields x2 and y2.
In this exercise, we will not determine whether the common points are points of intersection or points of tangency.
Additionally, we will omit the determination and display of whether the two parabolas are identical (completely overlapping)
or whether they have the same axis positions but different vertex heights (parallel but oriented up and down).