general equation of the ellipse

[feral widget]

Hi, I'm new, I'm not good at mathematics, I've been trying to do this problem for a while without success and I'll hand it in tomorrow. Could someone please help me :
Determine the general equation of the ellipse and construct its locus by writing down all the coordinates of its elements, if its foci are the points (-4,-2) (-4,-6) and the length of each straight side is equal to 6 units

[raven oyster]

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[keen hill]

the problem statement isn't that general.
if you're finding a really general solution, then simple.
it's so classic that you can find the entire proof online

with the general result, just substitute the numbers into the equation

https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_1e_(OpenStax)/08%3A_Analytic_Geometry/8.02%3A_The_Ellipse

this is an example textbook containing the said derivation

i suggest seeing this to learn the theory. the rest is just basic graph transformation

[feral widget]

Thank you very much for the helpful materials, I would like to treat you to a virtual pizza as a token of gratitude.🍕