Mathematics, 21.03.2020 01:43 roscoe53

The center of an ellipse is located at (3, 2) One focus is located at (6, 2) and its associated directrix is represented by the line x = 11 1/3 Given the standard form of the equation of an ellipse, what are the values of h, k, a, and b?

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Answer from: psychocatgirl1

Step-by-step explanation:

This is really hard to try and explain over the internet here, but I'll do my best, assuming you have some experience with ellipses.

We are given the center of (3, 2), and the focus of (6, 2). The focus is 3 units to the right of the center; the other focus is 3 units to the left of the center at (0, 2). The focus has coordinates of (-ae, 2) and (ae, 2) from left to right and the distance between them then is 2ae. There are 6 units between the 2 foci, so 2ae = 6.

The directrix is 8 1/3 units from the center to the right AND the left. The directrices have distances of 2a/e between them. There are 16 2/3 units between the 2 directrices, so

$\frac{2a}{e}=\frac{50}{3}$

We can solve for the eccentricity of this ellipse given the fact that the eccentricity is the ratio of the distance between the foci to the distance between the directrices. Therefore,

$\frac{2ae}{2\frac{a}{e} }=\frac{6}{\frac{50}{3} }$

The 2's andd the a's cancel, leaving you with

$e^2=\frac{18}{50}=\frac{9}{25}$

That gives us then that

$e=\frac{3}{5}$

Going back to the identity for the distance between the foci, 2ae = 6, we fill in e and solve for a:

$2a(\frac{3}{5})=6$ and

$\frac{6a}{5}=6$

which gives us that a = 5

Now use the identity b^2=a^2(1-e^2) to solve for b:

$b^2=25(1-\frac{9}{25})$ and

$b^2=25(\frac{16}{25})$ and

b = 4

Because this is a horizontally stretched ellipse, it is of the form

$\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1$

we fill in as

$\frac{(x-3)^2}{25}+\frac{(y-2)^2}{16}=1$

Again, since you are expected to be able to solve for the equation of an ellipse at this advanced level, I am assuming that the equations I gave above as a means to solve for the different characteristics of an ellipse are familiar to you. This is definitely NOT beginning conics!

Answer from: Quest

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.

Answer from: Quest

answer is 33

step-by-step explanation:

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