How to Calculate the Focal Point of a Parabola

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Finding the focal point of a parabola is a task you're likely to learn in a high school or college geometry class. A simple mathematical equation can lead you to the answer.

Things You'll Need

  • Ruler
  • Graph paper
  • Calculator (optional)
  • Measure the width of the parabola from rim to rim. You can measure the width with a ruler or by observing the markings on a piece of graph paper on which the parabola is drawn. Be sure all your measurements use the same units.

  • Find the radius of the parabola by dividing your answer from Step 1 in half. For instance, if the measurement in Step 1 was 20 centimeters, the radius would be 10 centimeters.

  • Square the radius. In this example, you would multiply 10 times 10 to get an answer of 100.

  • Find out how deep the parabola is by measuring from its vertex (lowest point) to the highest point of its two sides. For this example, consider the depth to be 10 centimeters.

  • Multiply the depth by 4. Therefore, you would have 10 times 4, which equals 40.

  • Divide your answer from Step 3 by your answer from Step 5. Your equation would be as follows: 100/40=2.5.

  • Use the answer from Step 6 to measure upward from the vertex in order to find the focal point. In this example, if your vertex was at 0, your focal point would be at 2.5 centimeters above the vertex.

References

  • Photo Credit Jupiterimages/Polka Dot/Getty Images
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