Engineering graphics parabola

@omprakash-Um9Ko0 • Oct 27, 2024

Oct 27, 2024

1.4K

A rectangle having 125x75 mm side inscribed with two parabolas in it with axis right angle to each other.How to Draw It.??? help

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Ramani Aswath

@ramani-VR4O43 • Jun 7, 2015

You have only three defining points, two corners and mid point of the opposite side. There can be an infinite number of parabolas passing through these points.
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omprakash patil

@omprakash-Um9Ko0 • Jun 7, 2015

Considering two cornerns and mid pt. Of opposite side there is only one possibility only single symmetric axis parabola will pass through it.
As corner ends will be lie on rectangle side END point and opposite side mid point. Will be the vertex.
Since we are not considering symmetric parabolas with infinite no. Of corner ends lie on rectangle side.
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Ramani Aswath

@ramani-VR4O43 • Jun 7, 2015

nooneperfect
Considering two cornerns and mid pt. Of opposite side there is only one possibility only single symmetric axis parabola will pass through it.
The only conic section uniquely defined by three points is a circle. Not true of other conic sections.
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omprakash patil

@omprakash-Um9Ko0 • Jun 7, 2015

No circle.will be not possible since it is rectangle it will not fit in corner and mid pt.
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omprakash patil

@omprakash-Um9Ko0 • Jun 7, 2015

This will be the solution i guess
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Ramani Aswath

@ramani-VR4O43 • Jun 7, 2015

There will be one circle that passes through the two corners of one side and the mid point of the opposite side. It will not be an inscribed complete circle but an arc. The second picture does denote one of possible infinite solutions.
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omprakash patil

@omprakash-Um9Ko0 • Jun 7, 2015

Yup.
But i will not say it has infinite solutions since problem statment is that it inscribe two parabolas which are in rectangle .
So as two corners and opposite side mid pt. Is only case.
Thx
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Ramani Aswath

@ramani-VR4O43 • Jun 7, 2015

nooneperfect
So as two corners and opposite side mid pt. Is only case.
Please go through conic sections in detail. There can be an infinite number of parabolas going through the same three points.
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omprakash patil

@omprakash-Um9Ko0 • Jun 7, 2015

Considering only Two corner and mid pt. 8n rectangle
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omprakash patil

@omprakash-Um9Ko0 • Jun 7, 2015

This can be true only as per ur point.
But if vertex as mid point consider then its only one parabola...
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Ramani Aswath

@ramani-VR4O43 • Jun 8, 2015

nooneperfect
A rectangle having 125x75 mm side inscribed with two parabolas in it with axis right angle to each other.
I agree if the additional constraint on the vertex is put. Otherwise one can have an infinity of two parabolas with perpendicular axes passing through the specified points.
If the vertex is the midpoint of the opposite side, then the solution is trivial. Make the vertex the origin and the axis as y axis. Then the parabola is y = ax^2. Determine a from one of the two end points and plot.
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omprakash patil

@omprakash-Um9Ko0 • Jun 8, 2015

Right Sir... with above constraint this will be solutionsolution what interpretations going in my Brain.thanks a lot ... i learned so much
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Ramani Aswath

@ramani-VR4O43 • Jun 8, 2015

nooneperfect
i learned so much
Both of us learnt a lot.
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