0
votes
1answer
28 views

The minimum distance from the circle $x^2+(y+6)^2=1$ to parabola $y^2=8x$?

What are the coordinates of the points on the parabola $y^2=8x$ which are at the minimum distance from the circle $x^2 + (y+6)^2=1$?
1
vote
3answers
106 views

How to find the point on a parabola where x and y are equal?

On a parabola how could i find the point at which the y and x points are equal and meet on a point of the graph, algebraically?
0
votes
0answers
29 views

Modelling rational power functions as cones for conic quadratic programming

It's quite easy to find documentation online that shows that conic quadratic programming can be used with functions that have ration powers, such as x^(3/2). example I can also find examples of these ...
1
vote
2answers
89 views

Minimizing area of a triangle with two fixed point and a point on parabola

A triangle is made up of three points, $A, B$, and $P$. $A(-1, 0)$ $B(0, 1)$ $P$ is a point on $y^2 = x$ Minimize the area of Triangle $ABP$. My approach is far too complicated, which ...
2
votes
1answer
449 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
457 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 ...
1
vote
0answers
90 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
1answer
73 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
340 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 ...