Geometrical Proof of the length of the Latus Rectum of the Parabolic Curve is equal to four times the distance of the focus from the vertex
| Vol-3 | Issue-10 | October 2018 | Published Online: 10 October 2018 PDF | ||
| Author(s) | ||
| Gill Amandeep Kaur 1 | ||
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1Assistant Professor in mathematics, SGGS College, Sector -26, Chandigarh, Punjab, India. |
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| Abstract | ||
| Since childhood we learn things from parents, teachers and surroundings. We may accept many things without reasoning or proofs. Though we never had time or intent to stop and analyze what we have learnt with deeper meaning. While studying, our focus is merely on achieving grades. Due to limitation of time, instead we mug up things. Many teachers never teach why the length of latus rectum is 4a for the parabola or even about the shape of parabola. As a student we thought it was easier to remember that length of latus rectum is 4a before solving any Parabola related problems. It never stuck us, WHY it is 4a? Similarly, Why is ? Why equation of X-axis is y=0 and Y- axis is x=0? Why in ellipse ? Why in hyperbola ? We never sit back, think and try to visualize, why? We just accept the things as it comes without reasoning and knowledge. We go on cramming things unknowingly. Now while teaching this topic, I came across an e- book, which made me think about the subject more deeply. It has encouraged me to write this topic, because it may encourage a few more teachers like me to understand the deep concept rather than just memorizing. Geometrically in mathematics, then it creates a great connection of abstract symbols to visual meanings. In this paper, I make an attempt to understand geometrically the length of Latus rectum is equal to four times the distance of the focus from the vertex. I have tried to explain what I have learnt with a few diagrams. | ||
| Keywords | ||
| Geometry, Parabola, Axis, Chord, Latus Rectum | ||
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