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⠀⠀⠀☞ 1)a) c = (4,-1), R = 5; b) c = (0,-1/2), R = 3; c) c = (1/2,-3), R = 4; d) c = (0,0), R = 5; 2)a) (x-2)²+(y-5)² = 9; b) (x² + (y-3)² = 4; c) (x-5)² + y² = 64; d) (x-3)² + (y+2)² = 49; e) x² + y² = 1/9; f) (x+2)² + (y-5)² = 9/16. ✅
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⠀⠀⠀⭐⠀Para realizar este exercício vamos rever a forma geral da equação reduzida da circunferência.⠀⭐⠀
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[tex]\Large\red{\boxed{\pink{\boxed{\begin{array}{lcr}\green{\star}&&\green{\star}\\&\!\!\orange{\sf (x - x_0)^2 + (y - y_0)^2 = R^2}\!\!&\\\green{\star}&&\green{\star}\\\end{array}}}}}[/tex]
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[tex]\text{\pink{$\Longrightarrow$}~\Large\orange{$\sf (x, y)~$}}[/tex] sendo as coordenadas dos pontos da circunferência;
[tex]\text{\pink{$\Longrightarrow$}~\Large\orange{$\sf (x_0, y_0)~$}}[/tex] sendo as coordenadas do centro da circunferência;
[tex]\text{\pink{$\Longrightarrow$}~\Large\orange{$\sf R~$}}[/tex] sendo o raio da circunferência.
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⠀⠀⠀➡️⠀Vejamos agora cada um dos itens:
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1) a) (x - 4)² + (y + 1)² = 25✍
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[tex]\blue{\Large\text{$\sf~~$}\begin{cases}~\text{$\sf\green{\boxed{\blue{\sf~c = (4, -1)~}}}$}\\\\~\text{$\sf\green{\boxed{\blue{\sf~R = 5~}}}$} \end{cases}}[/tex]⠀⠀✅
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1) b) x² + (y + 1/2)² = 9✍
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[tex]\blue{\Large\text{$\sf~~$}\begin{cases}~\text{$\sf\green{\boxed{\blue{\sf~c = (0, -1/2)~}}}$}\\\\~\text{$\sf\green{\boxed{\blue{\sf~R = 3~}}}$} \end{cases}}[/tex] ✅
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1) c) (x - 1/2)² + (y + 3)² = 16✍
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[tex]\blue{\Large\text{$\sf~~$}\begin{cases}~\text{$\sf\green{\boxed{\blue{\sf~c = (1/2, -3)~}}}$}\\\\~\text{$\sf\green{\boxed{\blue{\sf~R = 4~}}}$} \end{cases}}[/tex] ✅
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1) d) x² + y² = 25✍
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[tex]\blue{\Large\text{$\sf~~$}\begin{cases}~\text{$\sf\green{\boxed{\blue{\sf~c = (0, 0)~}}}$}\\\\~\text{$\sf\green{\boxed{\blue{\sf~R = 5~}}}$} \end{cases}}[/tex] ✅
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2) a) C = (2,5), R = 3✍
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[tex]\Large\green{\boxed{\rm~~~\gray{(x - 2)^2 + (y - 5)^2}~\pink{=}~\blue{ 9 }~~~}}[/tex] ✅
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2) b) C = (0,3), R = 2✍
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[tex]\Large\green{\boxed{\rm~~~\gray{x^2 + (y - 3)^2}~\pink{=}~\blue{ 4 }~~~}}[/tex] ✅
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2) c) C = (5,0), R = 8✍
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[tex]\Large\green{\boxed{\rm~~~\gray{(x - 5)^2 + y^2}~\pink{=}~\blue{ 64 }~~~}}[/tex] ✅
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2) d) C = (3,-2), R = 7✍
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[tex]\Large\green{\boxed{\rm~~~\gray{(x - 3)^2 + (y + 2)^2}~\pink{=}~\blue{ 49 }~~~}}[/tex] ✅
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2) e) C = (0,0), R = 1/3✍
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[tex]\Large\green{\boxed{\rm~~~\gray{x^2 + y^2}~\pink{=}~\blue{ 1/9 }~~~}}[/tex] ✅
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2) f) C = (-2,5), R = 3/4✍
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[tex]\Large\green{\boxed{\rm~~~\gray{(x + 2)^2 + (y - 5)^2}~\pink{=}~\blue{ 9/16 }~~~}}[/tex] ✅
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[tex]\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]☁
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⠀⠀☀️ L͎̙͖͉̥̳͖̭̟͊̀̏͒͑̓͊͗̋̈́ͅeia mais sobre equação da circunferência:
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https://brainly.com.br/tarefa/36551231 ✈
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[tex]\huge\blue{\text{\bf\quad Bons~estudos.}}[/tex] ☕
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[tex]\quad\qquad(\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios})[/tex] ☄
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[tex]\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }\LaTeX}[/tex]✍
[tex]\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly}[/tex] ☘☀❄☃☂☻)
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[tex]\Huge\green{\text{$\underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~}$}}[/tex] ✞
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