Equação da Elipse na forma reduzida

[LAZAROTTI]

Qual alternativa expressa a equação da elipse 16x²+9y²-64x-54y+1=0 na forma reduzida?

a)\(\frac{(x-2)^2}{9}+\frac{(y+3)^2}{16}=1\)

b)\(\frac{(x-2)^2}{9}+\frac{(y-3)^2}{16}=1\)

c)\(\frac{(x+2)^2}{9}+\frac{(y+3)^2}{16}=1\)

d)\(\frac{(x-2)^2}{16}+\frac{(y-3)^2}{9}=1\)

e)\(\frac{(x+2)^2}{9}+\frac{(y-3)^2}{16}=1\)

Obrigado!

[danjr5]

Qual alternativa expressa a equação da elipse 16x²+9y²-64x-54y+1=0 na forma reduzida?

a)\(\frac{(x-2)^2}{9}+\frac{(y+3)^2}{16}=1\)

b)\(\frac{(x-2)^2}{9}+\frac{(y-3)^2}{16}=1\)

c)\(\frac{(x+2)^2}{9}+\frac{(y+3)^2}{16}=1\)

d)\(\frac{(x-2)^2}{16}+\frac{(y-3)^2}{9}=1\)

e)\(\frac{(x+2)^2}{9}+\frac{(y-3)^2}{16}=1\)

Obrigado!

\(\\ 16x^2 + 9y^2 - 64x - 54y + 1 = 0 \\\\ 16x^2 - 64x + 9y^2 - 54y + 1 = 0 \\\\ (16x^2 - 64x) + (9y^2 - 54y) + 1 = 0 \\\\ (4x - 8)^2 - 64 + (3y - 9)^2 - 81 + 1 = 0 \\\\ [4(x - 2)]^2 + [3(y - 3)]^2 = 144 \\\\ 16(x - 2)^2 + 9(y - 3)^2 = 144 \,\,\,\, \div (144 \\\\ \fbox{\frac{(x - 2)^2}{9} + \frac{(y - 3)^2}{16} = 1}\)