# Tagged Questions

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### finding $\lambda$ when equation of parabola is given

If the equation $\lambda x^2 + 4xy + y^2 + \lambda x + 3y + 2 = 0$ represents a parabola. Then find $\lambda$. I got stuck in this question while solving parabola. Is here anybody who can help me ...
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### How to find the tangent vector for intersection of two cones?

Let two points $A=(x_{0},y_{0},z_{0})$ and $B=(x_{1},y_{1},z_{1})$ are given vertex of two cones and the generating angle of two cones are $m$. Intersection of two cones could be either an ellipse or ...
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### The probability of $Ax^2+Bxy+Cy^2 = 1$ defining an ellipse.

In Keith Kendig's paper, Stalking the Wild Ellipse (published in the American Mathematical Monthly, November 1995), he says that if $A, B, C$ are chosen at random, the probability that the Cartesian ...
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### Conics in $\mathbb{A}^2$

I'm trying to solve Exercise 3.1 in Hartshorne's Algebraic Geometry: Show that any conic in $\mathbb{A}^2$ is isomorphic to $\mathbb{A}^1$ or $\mathbb{A}^1-\{0\}$. I know from a previous exercise ...
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### Difficult equations to rewrite as ellipses

I have this equality that defines an elliptic boundary. I am trying to rewrite it in the form of the equation of an ellipse, but I am having trouble doing that. How would I go about rewriting this ...
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### A Hunt for a Mathematical Machine That Gives Points

The central question is : Is there any method for Producing the global Points on the curve (any cubic curve, or at least a Degree-2 curve ) , if we have local Part with us ? Explanation: ...
If we have a curve $C:\{ P(x,y) = 0 \}$ and define $\omega=\frac{\mathrm{d}x}{y}$ then is $$\int_0^A \omega + \int_0^B \omega = \int_0^{A \oplus B} \omega$$ (with $\oplus$ being addition on a group ...