Points of Intersection Between a Parabola and a Line
Author: shiroeExecutions: 385
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Enter a, b, c, m, and n.
Enter a non-zero number for a (no output will be generated if 0 is entered).
Output the number of common points.
Output the x and y coordinates of the common points.
Enter a non-zero number for a (no output will be generated if 0 is entered).
Output the number of common points.
Output the x and y coordinates of the common points.
| Number of common points | |
| The x-coordinate of point (1) | |
| The y-coordinate of point (1) | |
| The x-coordinate of point (2) | |
| The y-coordinate of point (2) |
When there is one common point, that point is a point of tangency.
Digit display setting: 50 digits. Digit count can be changed. Real number calculation mode.
Digit display setting: 50 digits. Digit count can be changed. Real number calculation mode.
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Consider the real xy-plane. (The y-axis is the vertical axis, and the x-axis is the horizontal axis.)
Assume the parabola is perpendicular to the y-axis.
Let the equation of the parabola be y = ax² + bx + c.
The equation of the line is in the form y = mx + n.
The number of common points is determined by the discriminant of the quadratic equation after eliminating y.