|
Question 1185705: Find the equation of the circle that passes through the point (9,7) and is tangent to both x and y axis and the line 3x-4y=24
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
There are too many constraints; no circle satisfies all of them.
-----------------------------------------------------------------------
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).
-----------------------------------------------------------------------
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.
|
|
|
| |
