# Tagged Questions

68 views

### Parameterizing a spherical cap in cylindrical coordinates

In calculating the mean curvature for a surface of the form $(f(z)\cos(\theta), f(z)\sin(\theta), z)$ I need to use some checks to ensure I haven't made any mistakes along the way. The one I would ...
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### which algebraic curves admit (nice?) geometric characterizations?

Caveat lector: this a super soft question. In an effort to help my students, across many different courses, better appreciate and put to work the distinction between geometric objects & ...
598 views

### Finding the locus of the midpoint of chord that subtends a right angle at $(\alpha,\beta)$

There is a circle $x^2+y^2=a^2$. On any line that cuts the circle in two distinct points(it is a secant), the points of intersection with circle are taken and at those two points I draw the tangents ...
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### Every conic in $\Bbb{P}^2$ equivalent to $XZ - Y^2$ - what is meant by hint here?

I am looking at Miles Reid's UAG book. There he claims that every projective conic is projectively equivalent to $XZ = Y^2$. He asks to show that $Q$ a non-degenerate quadratic form is such that ...
So if I have 2 points $A$ and $B$ such that $F(A) = (1; a, a^3)$, and $F(B) = (1; b, b^3)$. how do I find the equation of this line in homogeneous coordinates? So I know how to get a line the ...