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Question 650667: please help me solve this problem i am totally confused:
instructions are find the slopes of lines with a y-intercept of 1 tangent to the circle (x-3)^2 + y^2=4
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! instructions are find the slopes of lines with a y-intercept of 1 tangent to the circle (x-3)^2 + y^2=4
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The radius of the circle is 2.
The center of the circle is (3,0).
The distance from the y-int @ (0,1) to the center of the circle = sqrt(10).
The tangent lines from a right angles at each tangent point --> 2 right triangles with hypotenuse = sqrt(10) and a side = 2.
--> the distance from (0,1) to the tangent points = sqrt(6).
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The tangent points are the intersection of the given circle and a 2nd circle centered at (0,1) with radius = sqrt(6).
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The angle between the y-axis and the line from (3,0) to (0,1) = acot(1/3) =~ 71.565 degs.
The angle of the right triangle at (0,1) = arcsin(2/sqrt(10)) =~ 39.232 degs
The upper tangent line makes and angle with y-axis of the sum = 110.797 degs
The angle with the x-axis = 110.797 - 90 = 20.797 degs
The slope of the line = tan(20.797) = 0.38
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The calculations of the 2nd tangent line are similar.
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If you email via the Thank You note I can send a graph with makes it clearer.
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