Tagged Questions
2
votes
1answer
43 views
Minimum distance between $x = -y^2$ and $(0,-3)$
Find the minimum distance from the parabola $x + y^2 = 0$ (i.e. $x = -y^2$) to the point $(0,-3)$.
This is a homework question. When I try to use the derivative and substitute $-y^2$ for $x$, I ...
11
votes
2answers
385 views
2 circles and one ellipse and minimum area problem.
2 circles ($r_1 \neq r_2$) and one ellipse touch each other as shown in Figure-1. What is the minimum area (A) among them ? Please consider $a,b,r_1,r_2$ given values(constants). Let's imagine we ...
0
votes
0answers
54 views
History of calculus-based optimization
I would like to know:
- who started with calculus-based optimization problems and when it was,
- if there is a book focusing on history of ellipses/ conic sections
- if someone ever tried to ...
0
votes
0answers
75 views
Minimize the number of ellipses to cover a region
Suppose I have n ellipses, $\left\lbrace E_i \right\rbrace_{i=1}^n $; each ellipse, $E_i$, has the same area $A_1$. I want to completely cover a region (assume a rectangle) , $R$, with the least ...
0
votes
1answer
61 views
Optimization Problem with Modulus function
Any ideas how to solve the following problem:
$$Minimize: |F(x,y)|+|G(x,y)|$$ s.t. $x<A, y<B$
where $$F(x,y)=ax^2+by^2+cx+dy+e$$ $$G(x,y)=fx^2+gy^2+hx+iy+j$$
and $A,B$ are known constants.
Any ...
2
votes
1answer
157 views
Properties of Parabola / Optimization
I've been working through some past papers for an exam which I am due to be sitting tomorrow. In the Conic Sections paper from a couple of years ago, the following question came up:
The path of a ...
