Circles A and B have the following equations #(x -4 )^2+(y -8 )^2= 25 # and #(x -2 )^2+(y -7 )^2= 49 #. What is the greatest possible distance between a point on circle A and another point on circle B?

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Circles A and B have the following equations #(x -4 )^2+(y -8 )^2= 25 # and #(x -2 )^2+(y -7 )^2= 49 #. What is the greatest possible distance between a point on circle A and another point on circle B?

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Answer 1 · 2016-08-23T16:37:24

12+#sqrt5#

Explanation:

The general equation of a circle is #(x-a)^2+(y-b)^2=r^2#
Where the centre of the circle is(a,b) and the radius is r

The distance between the centres of the circles (4,8) and (2,7)
is #sqrt5#. The distance between the x coordinate is 2 , the distance between the y coordinates is 1 . From Pythagoras the distance is #sqrt((2^2+1^2)#
The radii of the circles are 5 and 7 hence the greatest possible distance.

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Circles A and B have the following equations #(x -4 )^2+(y -8 )^2= 25 # and #(x -2 )^2+(y -7 )^2= 49 #. What is the greatest possible distance between a point on circle A and another point on circle B?

1 Answer

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