Answer by Felix Marin for Find the curve of intersection between $x^2 + y^2 +...
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View ArticleAnswer by Ennar for Find the curve of intersection between $x^2 + y^2 + z^2 =...
I would go about this geometrically.First of all, the intersection is a circle. This is true in general for (non-tangent) intersection of plane and sphere. Here it is especially easy to see because the...
View ArticleAnswer by Donald Splutterwit for Find the curve of intersection between $x^2...
$2x^2+2xy+2y^2=1$ can be rewritten as $(2x+y)^2+3y^2=2$ and this can be parameterised \begin{eqnarray*}\frac{2x+y}{\sqrt{2}} &=& \cos \theta \\\sqrt{\frac{3}{2}} y &=& \sin \theta ....
View ArticleAnswer by Dr. Sonnhard Graubner for Find the curve of intersection between...
HINT: it is $$y_{1,2}=-\frac{x}{2}\pm\sqrt{\frac{1}{2}-\frac{3}{4}x^2}$$ and with that $y$ we can compue $z$
View ArticleFind the curve of intersection between $x^2 + y^2 + z^2 = 1$ and $x+y+z = 0$
Find the curve of intersection between $x^2 + y^2 + z^2 = 1$ and $x+y+z = 0$My attempt:$x^2 + y^2 + z^2 = 1$$x+y+z=0$$$(2) \implies z = -(x+y)$$$$(1) \implies x^2+y^2+(x+y)^2 = 1$$$$2x^2 + 2y^2 + 2xy =...
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