Question 1068273
Find an equation(s) of the circle(s) of radius 4 with center on the line 4x + 3y + 7 = 0 and tangent to 3x + 4y + 34 = 0
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There are 2 circles.
Find the equations of the 2 lines parallel to 3x + 4y + 34 = 0 and 4 units from it.
3x + 4y + 34 = 0
y = (-3/4)x - 17/2
Slope m of 3x + 4y + 34 = 0 is -3/4.
Difference in y-ints = 4/(cos(atan(-3/4)) = 5
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--> the 2 parallel lines are:
y = (-3/4)x - 17/2 + 5 = (-3/4)x - 7/2
and y = (-3/4)x - 17/2 - 5  = (-3/4)x - 27/2
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The intersection of those 2 lines and 4x + 3y + 7 = 0 are the 2 centers of the circles, (h,k).
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4x + 3y + 7 = 0
y = (-3/4)x - 7/2
4x -9x/4 - 21/2 = -7
7x/4 = 7/2
x = 2, y = -5
--> {{{(x-2)^2 + (y+5)^2 = 16}}}
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Find the other circle the same way.
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