Question

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19. Write the equation of the ellipse in standard form.

Answer 1

\[2(x+4)^{2}+3(y-1)^{2}=24\]

Answer 2

Foil out the (x+4)^2 and the (y-1)^2, then distribute your 2 and 3 accordingly. Standard form means you have no fractions, the terms are in descending order of powers, and the first term is positive

Answer 3

so (2x+8)^2 + (3y-3)^2

Answer 4

following order of operations, you need to square the terms in parentheses first
What the problem states is 2(x+4)(x+4) originally, but what you've done by distributing first is make that into (2x+8)(2x+8) which is completely different

Answer 5

hmmm, well, this would be an "ellipse standard form"....so \(\bf \cfrac{(x-h)^2}{a^2}+\cfrac{(y-k)^2}{b^2}=1\)

\(\bf 2(x+4)^{2}+3(y-1)^{2}=24\quad \textit{divide both sides by 24}\\ \quad \\
\cfrac{2(x+4)^2}{24}+\cfrac{3(y-1)^2}{24}=\cfrac{24}{24}\)

Answer 6

x+4)²/12 + (y-1)²/8 = 1 ?

Answer 7

simplify and that'd be the "ellipse standard form"

Answer 8

thank you

Answer 9

yeap \(\bf \cfrac{2(x+4)^2}{24}+\cfrac{3(y-1)^2}{24}=\cfrac{24}{24}\implies
\cfrac{(x+4)^2}{12}+\cfrac{(y-1)^2}{8}=1\)

Answer 10

yw