Question 1185705
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There are too many constraints; no circle satisfies all of them.<br>
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The graph of the line 3x-4y=24 lies in quadrants I, III, and IV.
To be tangent to both the x- and y-axes, the center of the circle must be on either the line y=x or the line y=-x.
So tangent to both the x- and y-axes and to the line 3x-4y=24, there is one circle in quadrant I, one in quadrant IV, and two in quadrant III.
None of them passes through the given point (9,7).<br>
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To be tangent to both the x- and y-axes, the center of the circle must be on either the line y=x or the line y=-x.
The given point (9,7) is in quadrant I, so the circle needs to be in quadrant I.
There are two circles in quadrant I that are tangent to the x- and y-axes and pass through (9,7).
Neither of them is tangent to the line 3x-4y=24.<br>