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 Jun 29, 2020
 #1
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If the line is tangent to the circle, then the line and the circle only touch at one point. That means if I solve for x( or y), there should only be one solution.

 

\(\begin{cases}x = 2y + 5\\x^2 + y^2 = 5\end{cases}\)

 

Substituting the first equation into the second, 

\((2y + 5)^2 + y^2 = 5\\ 4y^2 + 20y + 25 + y^2 = 5\\ 5y^2 + 20y + 20 = 0\\ y^2 + 4y + 4 = 0\\ (y + 2)^2 = 0\\ \boxed{y = -2}\)

 

As you see, it only has one solution. Therefore the line is indeed tangent to the circle.

 Jun 29, 2020
 #2
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0

i got 4/5 i am confused

Guest Jun 29, 2020
 #3
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0

Can you show me what you did to get 4/5?

MaxWong  Jun 29, 2020

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