The equation of the “tangent line to a parabola passing through a given point”
Author: shiroeExecutions: 53
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Enter the coefficients a, b, and c of the parabola's equation.
Enter a non-zero value for a.
Enter the x and y coordinates of a point where a tangent line is drawn to the parabola.
The program outputs the x-coordinate p1 and y-coordinate q1 of tangent point ①, the coefficient m1 representing the slope of tangent line ①, and the constant term n1.
If there are two tangent lines,
the program also outputs the x-coordinate p2 and y-coordinate q2 of tangent point ②, as well as the coefficient m2 representing the slope of tangent line ② and the constant term n2.
Enter a non-zero value for a.
Enter the x and y coordinates of a point where a tangent line is drawn to the parabola.
The program outputs the x-coordinate p1 and y-coordinate q1 of tangent point ①, the coefficient m1 representing the slope of tangent line ①, and the constant term n1.
If there are two tangent lines,
the program also outputs the x-coordinate p2 and y-coordinate q2 of tangent point ②, as well as the coefficient m2 representing the slope of tangent line ② and the constant term n2.
| p1 | (x-coordinate of the contact point) |
| q1 | (Y-coordinate of the contact point) |
| m1 | (Slope of a tangent) |
| n1 | (Constant term) |
| p2 | (x-coordinate of the contact point) |
| q2 | (Y-coordinate of the contact point) |
| m2 | (Slope of a tangent) |
| n2 | (Constant term) |
Digit display setting: 50 digits. Digit count can be changed. Real number calculation mode.
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Let the equation of the parabola be y = ax² + bx + c.
Let the x-coordinate of point ① be p1. Let the y-coordinate of point ① be q1.
Let the equation of tangent line ① be y = m1x + n1.
Let the x-coordinate of point of contact ② be p2. Let the y-coordinate of point of contact ② be q2.
Let the equation of tangent line ② be y = m2x + n2.