0
votes
1answer
67 views

Tangent at a singular point

I'm looking at this question If the tangent at the point $P$ with coordinates $(h, k)$ on the curve $y^2 = 2x^3$ is perpendicular to the line $4x = 3y$, find $(h, k).$ This is how I attempted it ...
1
vote
1answer
269 views

shortest distance between two points on $S^2$

Length of Curve in $2D$ is $l_{\gamma}(\mathbb{R}^2)=\int_{0}^{1}\sqrt{(dr/dt)^2+r^2(d\theta/dt)^2}$ Length of a curve in $3D$ is ...
-1
votes
1answer
141 views

Length of a curve on $S^2$

$1.$ Could any one tell me what is the shortest distance between $2$ points on $S^2$? $2.$ Could any one tell me how to measure explicitly a length of a curve on the $S^2$ using polar co-ordinates? ...
1
vote
1answer
157 views

Disk integration method to find volume of solid of revolution

I know that in a classic Cartesian coordinate system $xOy$, if I have a function $y = f(x)$ and I want to find the volume of the a solid of revolution around x-axis I can compute: $$V = \pi ...
2
votes
2answers
200 views

Rigorously showing there are infinitely many points of intersection?

I'm working on a problem that states if $k\geq 3$, $x,y\in\mathbb{R}^k$, $|x-y|=d>0$, and $r>0$, then (a) If $2r>d$, there are infinitely many $z\in\mathbb{R}^k$ such that ...
0
votes
1answer
63 views

Can any smooth planar curve which is closed, be a base for a 3 dimensional cone?

A cone in 3 dimensions has a vertex and a base. The contour of the base is a circle which is a smooth closed planar curve. Can there be a more general cone which can have any smooth closed planar ...