# Tagged Questions

Questions on conic sections and their properties; the curves formed by the intersection of a plane and a cone. Circles, ellipses, hyperbolas, and parabolas are examples of conic sections.

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### General Conic and its Rational Solutions

Suppose you have a rational conic $ax^2+bxy+cy^2+dx+ey+f=0$. There is a theorem that states if a conic has 1 rational solution it has infinitely many rational solutions. How can you prove this ...
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### Equation of tangent line to an ellipse, having a given angular coefficient

I've got to find the equations of the tangent lines to the ellipse: ${ x^2 / a^2 + y^2 / b^2 - 1 = 0 }$ having a given angular coefficient m that is a real number. I search for angular coefficient,...
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### Derive the length of the longest line segment that can be enclosed inside the region A.

Q. Let A be the region in the xy-plane given by A={(x,y): x=u+v, y=v, u^2+v^2≤1}. Derive the length of the longest line segment that can be enclosed inside region A. My attempt: I found the equation ...
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### Martini Glass - Extension

This is my extension to the very interesting question on the martini glass from 538.com by the Riddler as posted here earlier by MP Droid. Recap of original configuration. A martini glass has the ...
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### Proof of the Discriminant Law of Conics

Does anyone know a good resource and or know the proof for the Discriminant Law of Conics ($B^2 - 4AC > 0$ , Hyperbola ....) Thanks
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### Conics and conics of the form $ax^2+by^2+c=0$

The problem of finding rational points on conics is usually discussed (for example in the book of Silverman and Tate) for conics of the form $ax^2+by^2+c=0$. I assume that those conics are in ...
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### Find the minimum distance to move an ellipse to be inside another ellipse?

For the problem of ellipse intersection, I would like to know an accurate "general, including the cases of two non intersected ellipses, and non aligned ellipses" method to calculate the minimum ...