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B) there is a line with positive slope that is tangent to both circles. find the equation of this line, and (c) determine the points at which this tangent line touches each circ…
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B) there is a line with positive slope that is tangent to both circles. find the equation of this line, and (c) determine the points at which this tangent line touches each circ…
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May 25, 2018
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B) there is a line with positive slope that is tangent to both circles. find the equation of this line, and (c) determine the points at which this tangent line touches each circle
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Given that
there is a line with positive slope that is tangent to both circles
and
.
Let the point of tangency in the first circle be (a, b) and the point of tangency in the second circle be (c, d), then the slope of the tangent to the first circle is given by
and the slope of the second circle is given by
From the first circle equation, we have
and from the second equation, we have
Since the two slopes above are for the same line, then
Thus, we have
Terrabl
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May 31, 2018
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