 # Curved Lines  View Notes

## Meaning of Curved Lines

A curved line is defined as a line that is not straight but is bent. Ideally, a curved line holds a zero curvature and is continuous and smooth. Curves are prominent figures found everywhere around us. You can spot curves in an art or a decoration or a general thing, and curves are figures that can be seen everywhere around you. Curves were initially known as lines. However, to create a clear distinction between the concept of line and curve, lines are generally called as Straight Lines. Now, there is a distinction between a straight line and a curved line.

Curved Lines are frequently used in the graphical representation of functions as it is one of the vital topics in the field of Mathematics.

## Differentiate Between Curved Lines And Straight Lines

 Curved Line Straight Line A smoothly bent line which is not straight is called a Curved Line. The shortest line that joins any two points is called a Straight Line. The points determining a curved line change direction from one end to the next point. A straight line is a succession of multiple points aligned in the same direction. A curved line can be any line, whether straight or not. A straight line can be straight or curved. Curved Lines do not move in one direction. Straight Lines moves are one direction.

## Examples of Curved Lines

There are numerous curved line examples. The most common and prominent example of curved lines is the Alphabets- C and S. These letters of the alphabet are bent. In contrast, other letters like L, N, A, Z, and others are suitable examples of straight lines since they are neither curves but are joined segments of two or more consecutive lines.

## Types of Curved Lines

There are numerous and different types of curved lines. However, a few prominent types of curved line are-

### 1. Open Curve

A curved line or a curve is said to be open if the endpoints do not meet. In an open, cured line, the endpoints never meet.

A Parabola is a perfect example of an open curve line.

### 2. Closed Curve

A curve is stated to be closed if its starting point is the same as its ending point.

A circle or an eclipse is a perfect example of a closed curve line.

### 3. Simple Curve

A simple curve does not interact itself. Some curves are self-interacting; however, a simple curve line does not self-interact.

### 4. Algebraic Curve

An algebraic curve is a plane curve where a set of points are placed on the Euclidean plane and are represented in terms of polynomials. The degree of a curve is denoted by the polynomial’s degree.

For example- C = {(a, b) ∈ R2: P(a, b) = 0}

### 5. Transcendental Curve

A Transcendental Curve is different in its features from that of an Algebraic curve. A transcendental curve comprises an infinite number of inflexion points and multiple intersecting points which will be straight. It is not a polynomial in a and b points.

### What is an Isoquant Curve

The term Isoquant is an amalgamation of two terms- ‘Iso’ implies equal, and the word ‘quant’ refers to the quantity. Thus, the term isoquant is defined as a convex-shaped curve formed by the joining of the points. There are multiple and different factors that may be substituted for one another and are vital components to produce a good or product.

Q1. What is an Isoquant? State the Different Types of Isoquants.

The term isoquant is a sum of two words- ‘iso’ which infers as equal and ‘quant’ which implies quantity. Thus, the word ‘isoquant’ means constant output or the same volume at all points. An isoquant curve is a convex shaped curve formed by the joining of the points. These points depict the different blends of a production factor, resulting in a constant output.

Different Types of Isoquants

The Right Angle Isoquant Curve: This isoquant curve holds no substitution between the production factors.

The Convex Isoquant Curve: The convex Isoquant is smooth and convex to the origin. Here, the protection factors are substituted for each other.

The Linear Isoquant Curve: shows perfect substitutability between production factors, such that the quantities are produced either only as labour or capital.

Kinked Isoquant Curve: Here, there exists an assumption that only limited substitutability exists between the production factors.

Q2. Define Curved Lines. State the Types of Curved Lines.

A curved line is defined as a smoothly-flowing line that need not be necessarily straight but is bent. If the curvature of a line is zero, then the line is said to behave as a curved line.

Examples of curved lines- Alphabets like C, S, O, U, etc

There are multiple different types of curved lines- Open Curve: An open curve does not have any meeting endpoints.

Closed Curve: A closed curve has the same starting and ending points.

Simple Curve: A simple curve does not self-interact.

Algebraic Curve: An algebraic curve is a plane curve. Here, a set of points are placed on the Euclidean plane and are represented in terms of polynomials.

Transcendental Curve: A transcendental curve comprises an infinite number of inflexion points and multiple intersecting points which will be straight. It is not a polynomial in a and b points.

Q3. State the Differences Between a Straight Line and a Curved Line.

A Straight line is the shortest line that is joined by any two points, while a curved line is a smoothly-bent line which is not straight, but bent.

A Straight line moves in a particular direction (one direction), while curved lines do not move in a single direction.

A straight line is a succession of multiple points that are aligned in the same direction, while the points that determine curved lines change direction from one end to the next point. A straight line can be curved or straight, while a curved line can be any line, whether straight or not.

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