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38427889
Prova Circunferência e Elipse
Description
Prova sobre circunferência e elipse
No tags specified
circunferência
elipse
cálculo vetorial e geometria analítica
ensino superior
Quiz by
BOTE FÉ NA MATEMÁTICA
, updated more than 1 year ago
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Created by
BOTE FÉ NA MATEMÁTICA
over 1 year ago
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Resource summary
Question 1
Question
Encontre a equação da elipse cujos focos são \(F_1(-1, -3)\) e \(F_2(-1, 5)\) e excentricidade \(\frac{2}{3}\).
Answer
\(\frac{(x+1)^2}{20}+\frac{(y-1)^2}{36}=1\)
\(\frac{(x+1)^2}{36}+\frac{(y-1)^2}{20}=1\)
\(\frac{(x+1)^2}{5}+\frac{(y-1)^2}{9}=1\)
\(\frac{(x+1)^2}{9}+\frac{(y-1)^2}{5}=1\)
\(\frac{(x-1)^2}{20}+\frac{(y+1)^2}{36}=1\)
Question 2
Question
Encontre a equação da elipse cujos focos são \(F_1(1, -3)\) e \(F_2(1, 5)\) e excentricidade \(\frac{2}{3}\).
Answer
\(\frac{(x-1)^2}{20}+\frac{(y-1)^2}{36}=1\)
\(\frac{(x-1)^2}{36}+\frac{(y-1)^2}{20}=1\)
\(\frac{(x-1)^2}{5}+\frac{(y-1)^2}{9}=1\)
\(\frac{(x-1)^2}{9}+\frac{(y-1)^2}{5}=1\)
\(\frac{(x+1)^2}{20}+\frac{(y+1)^2}{36}=1\)
Question 3
Question
Encontre a equação da elipse cujos focos são \(F_1(-3, -1)\) e \(F_2(5, -1)\) e excentricidade \(\frac{2}{3}\).
Answer
\(\frac{(x-1)^2}{36}+\frac{(y+1)^2}{20}=1\)
\(\frac{(x-1)^2}{9}+\frac{(y+1)^2}{5}=1\)
\(\frac{(x-1)^2}{20}+\frac{(y+1)^2}{36}=1\)
\(\frac{(x-1)^2}{5}+\frac{(y+1)^2}{9}=1\)
\(\frac{(x+1)^2}{36}+\frac{(y-1)^2}{20}=1\)
Question 4
Question
Marque a alternativa que tem os focos da elipse com dois vértices \(A_1(3, -4)\) e \(A_2(3, 4)\) e distância focal 4.
Answer
\(F_1(3, 2)\) e \(F_2(3, -2)\)
\(F_1(2, 3)\) e \(F_2(-2, 3)\)
\(F_1(3, 4)\) e \(F_2(3, -4)\)
\(F_1(4, 3)\) e \(F_2(-4, 3)\)
Question 5
Question
Marque a alternativa que tem os focos da elipse com dois vértices \(A_1(1, -4)\) e \(A_2(1, 4)\) e distância focal 4.
Answer
\(F_1(1, 2)\) e \(F_2(1, -2)\)
\(F_1(2, 1)\) e \(F_2(-2, 1)\)
\(F_1(1, 4)\) e \(F_2(1, -4)\)
\(F_1(4, 1)\) e \(F_2(1, -2)\)
Question 6
Question
Dada a circunferência de equação \(x^2+y^2-6x = -5\), marque a alternativa que fornece o raio e o centro dessa circunferência.
Answer
\(r=2\) e C = (3, 0)
\(r=2\) e C = (0, 3)
\(r=4\) e C = (3, 0)
\(r=4\) e C = (0, 3)
Question 7
Question
Marque a alternativa que fornece a equação da circunferência dada na imagem
Image:
Questao+Prova (binary/octet-stream)
Answer
\((x+3)^2 + (y-3)^2 = 18\)
\((x-3)^2 + (y+3)^2 = 18\)
\((x+3)^2 + (y-3)^2 = 3\sqrt{2}\)
\((x-3)^2 + (y+3)^2 = 3\sqrt{2}\)
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