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Two circles of radius 1 are centered at  (4,0) and (-4,0) How many circles are tangent to both of the given circles and also pass through the point (0,5)?

 Mar 3, 2020

Best Answer 

 #2
avatar+24388 
+2

Two circles of radius 1 are centered at  (4,0) and (-4,0)

How many circles are tangent to both of the given circles and also pass through the point (0,5)?

 

There are 4 circles.
\(\begin{array}{|l|lcll|} \hline 1 & x^2+\left(y-\dfrac{5}{3}\right)^2=\left(\dfrac{10}{3}\right)^2 \\ \hline 2 & \left(x+1.0328\right)^2+\left(y-1\right)^2\ =\ \left(4.13118\right)^2 \\ \hline 3 & \left(x-1.0328\right)^2+\left(y-1\right)^2=\left(4.13118\right)^2 \\ \hline 4 & x^2+y^2=5^2 \\ \hline \end{array}\)

 

 

laugh

 Mar 4, 2020
 #1
avatar
0

There are only 2 such circles.  Try drawing the diagram in the coordinate plane.

 Mar 4, 2020
 #2
avatar+24388 
+2
Best Answer

Two circles of radius 1 are centered at  (4,0) and (-4,0)

How many circles are tangent to both of the given circles and also pass through the point (0,5)?

 

There are 4 circles.
\(\begin{array}{|l|lcll|} \hline 1 & x^2+\left(y-\dfrac{5}{3}\right)^2=\left(\dfrac{10}{3}\right)^2 \\ \hline 2 & \left(x+1.0328\right)^2+\left(y-1\right)^2\ =\ \left(4.13118\right)^2 \\ \hline 3 & \left(x-1.0328\right)^2+\left(y-1\right)^2=\left(4.13118\right)^2 \\ \hline 4 & x^2+y^2=5^2 \\ \hline \end{array}\)

 

 

laugh

heureka Mar 4, 2020
 #3
avatar+109499 
+1

Nice, heureka  !!!

 

 

cool cool cool

CPhill  Mar 4, 2020
 #4
avatar+24388 
+2

Thank you, CPhill !

 

laugh

heureka  Mar 5, 2020

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