In the equation #x^2 + (y-k)^2 = 16#, for what values of K is this circle tangent to y = 3?

Answer 1

#x^2+(y+1)^2 = 16#

or

#x^2 + (y-7)^2 = 16#

Standard form for the equation of a circle is

#(x-a)^2 + (y-b)^2 = r^2#
From this we can see that #r^2 = 16 implies r = 4#
#y=3#, horizontal line across at this level so we need the top (or bottom) of the circle to be at #y=3#. The radius is 4 so we want the centre of the circle to be 4 below #y=3#, ie #y=-1# or 4 above #y=3#, ie #y=7#
Therefore #k=-1# or #k=7#
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Answer 2

The circle is tangent to y = 3 when k = 3 ± 4.

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Answer from HIX Tutor

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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