Attractive problem

Equilateral triangles of sides $1, 3, 5, …, 2n-1$ , are placed end-to-end along a straight line.

Show that the vertices which do not lie on the line all lie on a parabola and that their focal radii are all integers.

#Geometry #ConicSections #JEE #Focii

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
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Comments

That's so beautiful! Thanks for sharing :)

Shashwat Shukla - 6 years, 3 months ago

Hi Megh

Is the equation of the parabola : $y^{2} = 3(x+\frac{1}{4})$ ?

A Former Brilliant Member - 6 years, 3 months ago

Ok,then?

U Z - 6 years, 3 months ago

Ok, I'll try posting a proof later on :)

A Former Brilliant Member - 6 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$