How To Find Tangents and Normals?
To find the Tangents and Normals to a curve we require the equation of the curve and the point at which we have to find the tangent and normal. Suppose the point at which we require to find the equation of the Tangents and Normals to the curve is (x1, y1) and the equation of the curve is f(x) then we can easily find the equation of the tangent and normal to the curve.
We know that the tangents and the normal are perpendicular to each other and the slope of the curve y = f(x) at any point (x1, y1) is given using the formula,
m = (dy/dx) at (x1, y1)
We also know that if the slope of the tangent line is m1 and the slope of the perpendicular line is m2 then,
m1 × m2 = -1
Using these we can easily find the tangent and normal to any curve of the circle.
Tangents and Normals
Tangent and Normals are the lines that are used to define various properties of the curves. We define tangent as the line which touches the circle only at one point and normal is the line that is perpendicular to the tangent at the point of tangency. Any tangent of the curve passing through the point (x1, y1) is of the form y – y1 = m(x-x1) and the equation of the normal at that point is represented using y – y1 = -1/m(x-x1) where m is the slope of the line.
Tangents and normals are lines related to curves. A tangent is a line that touches a curve at a specific point without crossing it at that point, and every point on a curve has its tangent. A normal, on the other hand, is a line that is perpendicular to the tangent at the point where the tangent contacts the curve.
Let us learn more about the equation of tangents and normals for various curves like circles, parabolas, and other curves, examples, and others in this article.
Table of Content
- What are Tangents and Normals?
- What are Tangents?
- Tangent Definition
- Properties of Tangents
- What are Normal?
- Normal Definition
- Properties of Normals
- How To Find Tangents and Normals?
- Equation of Tangent and Normal to the Curve
- In Cartesian Coordinates System
- In Parametric Form
- Tangents and Normals for Various Curves
- Practice Problems on Tangents and Normals
- Tangents And Normals Examples
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