I fixed this i found that the center was (1,2).You made a mistake right at the start, changing
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to
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Also, I wouldn't use inverse trig functions, which restrict the domain of x and y. Instead, I'd just solve for sine and cosine of 2t and use the Pythagorean identity. That also saves much of the second page.
But after you fix this, please define the "center" of a curve. What is it that you are finding on the last page, and how do you know that your work does that?
That's correct.I have
I fixed this i found that the center was (1,2).
The center of a conic section is the point midway between the foci.
We learned in school to find the center of a conic section using partial derivatives of their formula in cartesian form.
This is why i found the cartesian equation of the given conic.
Thank youThat's correct.
I'm not familiar with that method for finding the center, though I can see that it works, when the equation is in the right form. Having found that form, I would just complete the square and get more details about it: 4(x-1)^2+(y-2)^2=4.