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show that the circle x2+y2-16x-20y+115=0 and x2+y2+8x-10y+5=0 are tangent .

 Nov 12, 2019

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 #1
avatar+19913 
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Find the centers of the circles

x^2-16x +64     +y^2 -20 y +100    +115 -64 -100 = 0

(x-8)^2   + (y-10)^2  = 49

center (8,10)   radius = 7

 

x^2+8x + 16    + y^2-10y +25   +5 -16-25 =0

(x+4)^2   + (y-5)^2 = 36

center (-4,5)    radius = 6

 

Does the distance between the centers = the radii combined?   If so, they are tangent...

 

d^2 = (8--4)^2 + (10-5)^2

           144      + 25

d = 13        radii = 6+7 = 13       Yeas they are tangent....they touch at one point.

 Nov 12, 2019
 #1
avatar+19913 
+2
Best Answer

Find the centers of the circles

x^2-16x +64     +y^2 -20 y +100    +115 -64 -100 = 0

(x-8)^2   + (y-10)^2  = 49

center (8,10)   radius = 7

 

x^2+8x + 16    + y^2-10y +25   +5 -16-25 =0

(x+4)^2   + (y-5)^2 = 36

center (-4,5)    radius = 6

 

Does the distance between the centers = the radii combined?   If so, they are tangent...

 

d^2 = (8--4)^2 + (10-5)^2

           144      + 25

d = 13        radii = 6+7 = 13       Yeas they are tangent....they touch at one point.

ElectricPavlov Nov 12, 2019

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