query: How can one verify the equivalence between the geometric and algebraic definitions of an ellipse/hyperbola?
positive_passages.docid: 156827
positive_passages.text: Prove that the directrix-focus and focus-focus definitions are equivalent
negative_passages.docid: 103378
negative_passages.text: What is a composition of two binary relations geometrically?
negative_passages.docid: 115295
negative_passages.text: Why are the two dot product definitions equal?
negative_passages.docid: 47845
negative_passages.text: Mirror algorithm for computing $\pi$ and $e$ - does it hint on some connection between them?
negative_passages.docid: 106496
negative_passages.text: Open source computer algebra systems for general relativity
negative_passages.docid: 25526
negative_passages.text: How to use the Extended Euclidean Algorithm manually?
negative_passages.docid: 84189
negative_passages.text: Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
negative_passages.docid: 128598
negative_passages.text: How to prove this is a metric?
negative_passages.docid: 131080
negative_passages.text: Geometric representation of the sum of a Geometric Series
negative_passages.docid: 126040
negative_passages.text: Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$
negative_passages.docid: 7306
negative_passages.text: How is the equation of motion on an ellipse derived?
negative_passages.docid: 11875
negative_passages.text: how to calculate the bounding square of an ellipse?
negative_passages.docid: 4343
negative_passages.text: Conformal parametrization of an ellipse
negative_passages.docid: 131359
negative_passages.text: Determining if two geometric figures are approximately equal using PostGIS?
negative_passages.docid: 71074
negative_passages.text: The locus of the intersection point of two perpendicular tangents to a given ellipse
negative_passages.docid: 142862
negative_passages.text: Intersection of an ellipsoid and plane in parametric form
negative_passages.docid: 13954
negative_passages.text: Calculating the length of the semi-major axis from the general equation of an ellipse