A equação da tangente ao círculo x2 + y2= 25 no ponto (3,4) é:
Escolha uma:
a. 4x + 3y = 5
b. -3x +4y = -25
c. 4x + 3y = 25
d. 3x – 4y = 25
e. 3x +4y = 25
Respostas
respondido por:
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Boa tarde!
Solução!
![C(0,0)\\\\\
B(3,4)\\\\\\
Coeficiente~~angular\\\\\\\
m= \dfrac{yB-Yc}{Xb-Xc}\\\\\\
m= \dfrac{4-0}{3-0}\\\\\\
ms= \frac{4}{3}\\\\\\\\\\\
A ~~reta~~ tangente ~~e~~ perpendicular~~ a~~ reta ~~que~~ liga~~o ponto~~(3,4)\\\\\
mr.ms=-1 \\\\\\
mr= \dfrac{-1}{ms} \\\\\\
mr= \dfrac{-1}{ \dfrac{4}{3} }\\\\\
mr=-1. \frac{3}{4} \\\\\\
mr= \dfrac{-3}{4}](https://tex.z-dn.net/?f=C%280%2C0%29%5C%5C%5C%5C%5C%0AB%283%2C4%29%5C%5C%5C%5C%5C%5C%0ACoeficiente%7E%7Eangular%5C%5C%5C%5C%5C%5C%5C%0Am%3D+%5Cdfrac%7ByB-Yc%7D%7BXb-Xc%7D%5C%5C%5C%5C%5C%5C%0A%0A%0Am%3D+%5Cdfrac%7B4-0%7D%7B3-0%7D%5C%5C%5C%5C%5C%5C%0Ams%3D+%5Cfrac%7B4%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0AA+%7E%7Ereta%7E%7E+tangente+%7E%7Ee%7E%7E+perpendicular%7E%7E+a%7E%7E+reta+%7E%7Eque%7E%7E+liga%7E%7Eo+ponto%7E%7E%283%2C4%29%5C%5C%5C%5C%5C%0Amr.ms%3D-1+%5C%5C%5C%5C%5C%5C%0Amr%3D+%5Cdfrac%7B-1%7D%7Bms%7D+%5C%5C%5C%5C%5C%5C%0Amr%3D+%5Cdfrac%7B-1%7D%7B+%5Cdfrac%7B4%7D%7B3%7D+%7D%5C%5C%5C%5C%5C%0Amr%3D-1.+%5Cfrac%7B3%7D%7B4%7D+%5C%5C%5C%5C%5C%5C%0Amr%3D+%5Cdfrac%7B-3%7D%7B4%7D++%0A%0A%0A+ "C(0,0)\\\\\
B(3,4)\\\\\\
Coeficiente~~angular\\\\\\\
m= \dfrac{yB-Yc}{Xb-Xc}\\\\\\
m= \dfrac{4-0}{3-0}\\\\\\
ms= \frac{4}{3}\\\\\\\\\\\
A ~~reta~~ tangente ~~e~~ perpendicular~~ a~~ reta ~~que~~ liga~~o ponto~~(3,4)\\\\\
mr.ms=-1 \\\\\\
mr= \dfrac{-1}{ms} \\\\\\
mr= \dfrac{-1}{ \dfrac{4}{3} }\\\\\
mr=-1. \frac{3}{4} \\\\\\
mr= \dfrac{-3}{4}")
![y-4= \frac{-3}{4}(x-3)\\\\
y-4= \frac{-3}{4}(x-3)\\\\
y-4=\frac{-3x}{4} + \frac{9}{4}\\\\\\
4y-16=-3x+9\\\\\
3x+4y=9+16\\\\\\
3x+4y=25\\\\\\\\\\
\boxed{Resposta:3x+4y=25~~Alternativa~~e}](https://tex.z-dn.net/?f=y-4%3D+%5Cfrac%7B-3%7D%7B4%7D%28x-3%29%5C%5C%5C%5C%0Ay-4%3D+%5Cfrac%7B-3%7D%7B4%7D%28x-3%29%5C%5C%5C%5C+%0Ay-4%3D%5Cfrac%7B-3x%7D%7B4%7D+%2B+%5Cfrac%7B9%7D%7B4%7D%5C%5C%5C%5C%5C%5C%0A4y-16%3D-3x%2B9%5C%5C%5C%5C%5C%0A3x%2B4y%3D9%2B16%5C%5C%5C%5C%5C%5C%0A3x%2B4y%3D25%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Cboxed%7BResposta%3A3x%2B4y%3D25%7E%7EAlternativa%7E%7Ee%7D+ "y-4= \frac{-3}{4}(x-3)\\\\
y-4= \frac{-3}{4}(x-3)\\\\
y-4=\frac{-3x}{4} + \frac{9}{4}\\\\\\
4y-16=-3x+9\\\\\
3x+4y=9+16\\\\\\
3x+4y=25\\\\\\\\\\
\boxed{Resposta:3x+4y=25~~Alternativa~~e}")
Boa tarde!
Bons estudos!
Solução!
Boa tarde!
Bons estudos!
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