Question

Dê as equação da elipse que passa pelos pontos (2,0),(-2,0) e (0,1)
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Answer 1

$\displaystyle \underline{\text{Equa{\c c}{\~a}o da Elipse}}: \\\\ \sf \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \\\\\\ \underline{\text{Equa{\c c}{\~a}o da Elipse passando pelos pontos}}\ (2,0) \ (-2,0) \ e \ (0,1):\\\\ (2,0)\to \frac{2^2}{a^2}+\frac{0^2}{b^2}=1 \to a^2 = 4 \\\\\\ (0,1)\to \frac{0^2}{a^2}+\frac{1}{b^2}=1\to b^2=1 \\\\\\ \underline{\text{Equa{\c c}{\~a}o da Elipse}}: \\\\\\ \huge\boxed{\ \sf \frac{x^2}{4}+\frac{y^2}{1}=1\ }\checkmark$