Find an equation for the collection of points for which the distance to is twice the distance to

area, which i know how to do, im really just struggling with coming up with an equation

have done the calculus which reveals that the surface area is at a minimum when height is double the radius. I am now trying to find an equation for the relationship between the amount of wasted surface area as a percentage of the minimum surface area and the ratio between height and radius. If I were to plot it on a graph, the y axis would be the percentage of excess materials needed as a percentage of the minimum possible surface area, and the x axis would be height divided by radius. Since the surface area is minimized when height=2(radius), I know that when x=2, y=0. The website https://www.datagenetics.com/blog/august12014/index.html explains what I am trying to do quite well and shows the graph below. I am trying to find the equation for this graph, but am unsure how to go about it.

seen an equation of a circle this is moved in both the x and y direction be converted to a polar equation. For example, I know that the equation of a circle x^(2)+(y-2)^(2)=4 is r=4sin(theta) when converted to polar. Same thing for a translation with the x variable. However, I have never seen, nor do I know how to do, a conversion of a circle with both translations. For example, converting this equation of a circle to a polar equation: (x+3)^(2)+(y-4)^(2)=4. I have no idea how to do such a thing and cannot find any examples of such. Hope you can shed some light on this, Thanks.

three different equations for this problem but I can find and solve for the rest after that.

to the line x = -9.

such that when R is revolved about the line y=k, the resulting solid has the same volume as the solid resulting when R is rotated about the x-axis. Write an equation involving integral expressions that can be used to find the value of k, and then solve for k.

l unemployment rate dropped to about 4%. Find the average decline/year in unemployment rate from 2010 to 2018. Let x be the year since 2010 and y be the unemployment rate. Write an equation for unemployment rate versus year. Use your equation to estimate the unemployment rate in 2020.

The fees for the trip included a guide's fee as well as charge of $35 per person. The total cost for the group was $425. a) Write an equation in slope-intercept form to find the total cost C for p people. b) How much would it cost for