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THE FEUTEX TOOLKIT

Ellipse Tangent at Parametric Angle

Locate an ellipse point and its tangent line without a vertical-slope singularity.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
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FormulaX = a*cos(t*PI/180); Y = b*sin(t*PI/180); Line A = cos(t*PI/180)/a; Line B = sin(t*PI/180)/b
Sources and model references

Made for real tasks

  • Locate an ellipse point and its tangent line without a vertical-slope singularity.
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Worked example

Inputs

Horizontal semi-axis
5 length
Vertical semi-axis
3 length
Parametric angle
30 degrees

Expected results

X
4.330127019 length
Y
1.5 length
Line A
0.1732050808 1/length
Line B
0.1666666667 1/length

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter horizontal semi-axis, vertical semi-axis, parametric angle.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "a": 5,
  "b": 3,
  "t": 30
}

Accuracy and scope

Centered, axis-aligned ellipse. Tangent equation is line_a*x + line_b*y = 1.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.