Intersecção Parábola e Reta
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
intersec
About this calculator
The parabola and line intersection calculator is an online tool that helps find the intersection points between a parabola and a line. The parabola is defined by the equation ax²+bx+c, while the line is defined by the equation mx+n.
The calculator uses the formula ax²+(b−m)x+(c−n)=0 to find the intersection points. This formula is obtained by equating the two equations and rearranging the terms.
The intersection between a parabola and a line is common in mathematics and physics problems, especially in motion and optics problems. For example, in an optics problem, we may need to find the point at which a light ray intersects a parabolic surface.
When using this calculator, it is essential to be careful with the coefficients a, b, c, m, and n, as they must be entered correctly to obtain accurate results. Additionally, it is crucial to verify if the parabola and line actually intersect, as in some cases, they may be parallel or have no intersection points.
Frequently asked questions
What is a parabola?
A parabola is a U-shaped curve that can be defined by a quadratic equation of the form ax²+bx+c. It is common in mathematics and physics problems.
How to find the intersection points?
To find the intersection points between a parabola and a line, simply equate the two equations and solve for x. Then, substitute the x values into the original equations to find the corresponding y values.
What are the common use cases?
The common use cases include optics, motion, and physics problems, especially when dealing with parabolic surfaces and light rays.
What to do if the parabola and line are parallel?
If the parabola and line are parallel, they will not have intersection points. In this case, the calculator will not return valid results.