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Mate math help pls

 Feb 16, 2019
 #1
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\(\text{circle is centered at }(0,-8) \text{ and passes through }(2,-5)\)

 

\(\text{well it's easy enough to write down }\\ (x-0)^2 + (y-(-8))^2 = r^2\\ x^2 + (y+8)^2 = r^2\)

 

\(\text{but how to find }r^2 ?\\ \text{well every point on the circle is }r \text{ from the center}\)

 

\(r = \sqrt{(0-2)^2 + (-8 - (-5))^2} = \sqrt{4+9}=\sqrt{13}\\ \text{so we have}\\ x^2 + (y+8)^2 = 13\)

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 Feb 16, 2019
 #2
avatar+4455 
+1

For problem 4 you should be able to immediately see the radius of the circle described by that equation is \(\sqrt{12} = 2\sqrt{3}\)

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 Feb 16, 2019
 #3
avatar+4455 
+1

\(x^2 + 6x + y^2 + 6y = 18\\ \text{complete the square in both }x \text{ and }y\\ (x+3)^2 - 9 + (y+3)^2 -9 = 18\\ (x+3)^2 + (y+3)^2= 36 = 6^2\\ \text{the center can be read off directly as }(-3, -3)\)

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 Feb 16, 2019

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