Just by cutting a cone with a plane, you can get many interesting curves, the conic sections! Try our conic section calculator to know the types of conic sections and how to calculate their eccentricity, and much more!
Just by cutting a cone with a plane, you can obtain many interesting curves known as conic sections. These include the circle, ellipse, parabola, and hyperbola. Conic sections are fundamental in mathematics and appear in various fields such as astronomy, physics, engineering, and architecture.
Our Conic Sections Calculator allows you to explore these fascinating curves by calculating their eccentricity and deriving their standard equations based on your input parameters. Dive into the world of conic sections and discover their unique properties and applications.
Select the Conic Section Type:
Enter the Required Parameters:
Click "Calculate" to compute:
Review the Results displayed below the calculator.
The calculator performs the following checks on user inputs:
If invalid inputs are provided, an error message will be displayed, and calculations will be halted until valid inputs are entered.
The eccentricity () is a key parameter that defines the shape of a conic section, indicating how much it deviates from being circular.
Here's how the calculator computes the eccentricity and equations:
For Circle:
For Ellipse:
For Parabola:
For Hyperbola:
Edge Cases:
Conic sections have wide-ranging applications:
Astronomy:
Physics:
Engineering:
Architecture:
Optics:
Other curves and shapes might be considered depending on the application:
The exploration of conic sections dates back over two millennia:
Conic sections have played a pivotal role in the advancement of mathematics, physics, and engineering, influencing modern technologies and scientific understanding.
1' VBA Function to Calculate Eccentricity of a Hyperbola
2Function HyperbolaEccentricity(a As Double, b As Double) As Double
3 If a <= 0 Or b <= 0 Then
4 HyperbolaEccentricity = CVErr(xlErrValue)
5 ElseIf a <= b Then
6 HyperbolaEccentricity = CVErr(xlErrValue)
7 Else
8 HyperbolaEccentricity = Sqr(1 + (b ^ 2) / (a ^ 2))
9 End If
10End Function
11' Usage in Excel:
12' =HyperbolaEccentricity(5, 3)
131import math
2
3def ellipse_eccentricity(a, b):
4 if a <= 0 or b <= 0 or b > a:
5 raise ValueError("Invalid parameters: Ensure that a >= b > 0")
6 e = math.sqrt(1 - (b ** 2) / (a ** 2))
7 return e
8
9## Example usage:
10a = 5.0 # Semi-major axis
11b = 3.0 # Semi-minor axis
12ecc = ellipse_eccentricity(a, b)
13print(f"Eccentricity of the ellipse: {ecc:.4f}")
141function calculateEccentricity(a, b) {
2 if (a <= 0 || b <= 0 || b > a) {
3 throw new Error("Invalid parameters: a must be >= b > 0");
4 }
5 const e = Math.sqrt(1 - (b ** 2) / (a ** 2));
6 return e;
7}
8
9// Example usage:
10const a = 5;
11const b = 3;
12const eccentricity = calculateEccentricity(a, b);
13console.log(`Eccentricity: ${eccentricity.toFixed(4)}`);
141% MATLAB Script to Calculate Eccentricity of a Parabola
2% For a parabola, the eccentricity is always 1
3e = 1;
4fprintf('Eccentricity of the parabola: %.4f\n', e);
51using System;
2
3class ConicSection
4{
5 public static double ParabolaEccentricity()
6 {
7 return 1.0;
8 }
9
10 static void Main()
11 {
12 double eccentricity = ParabolaEccentricity();
13 Console.WriteLine($"Eccentricity of a parabola: {eccentricity}");
14 }
15}
161public class ConicSectionCalculator {
2 public static double calculateCircleEccentricity() {
3 return 0.0;
4 }
5
6 public static void main(String[] args) {
7 double e = calculateCircleEccentricity();
8 System.out.printf("Eccentricity of a circle: %.4f%n", e);
9 }
10}
111fn hyperbola_eccentricity(a: f64, b: f64) -> Result<f64, &'static str> {
2 if a <= 0.0 || b <= 0.0 || a <= b {
3 Err("Invalid parameters: a must be > b > 0")
4 } else {
5 Ok((1.0 + (b.powi(2) / a.powi(2))).sqrt())
6 }
7}
8
9fn main() {
10 let a = 5.0;
11 let b = 3.0;
12 match hyperbola_eccentricity(a, b) {
13 Ok(eccentricity) => println!("Eccentricity: {:.4}", eccentricity),
14 Err(e) => println!("Error: {}", e),
15 }
16}
17Circle:
Ellipse:
Parabola:
Hyperbola:
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