Two circles have the following equations: #(x -8 )^2+(y -5 )^2= 64 # and #(x +4 )^2+(y +2 )^2= 25 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
No overlap, greatest distance ≈ 26.89 units
• If sum of radii > d , then circles overlap
• If sum of radii < d , then no overlap
• If diff. of radii > d , then 1 circle inside other
We require to find the centres and radii of the circles.
#color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y- b)^2=r^2)color(white)(2/2)|)))# where (a ,b) are the coordinates of the centre and r, the radius.
sum of radii = 8 + 5 = 13
and diff. of radii = 8 - 5 = 3
Since diff. of radii < d , then 1 circle NOT inside the other
Since sum of radii < d , then no overlap of circles
Greatest distance between 2 points = sum of radii + d
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The circles do not contain each other. The greatest possible distance between a point on one circle and another point on the other is the sum of their radii.
The radius of the first circle is ( \sqrt{64} = 8 ).
The radius of the second circle is ( \sqrt{25} = 5 ).
Therefore, the greatest possible distance between a point on one circle and another point on the other is ( 8 + 5 = 13 ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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