What is the equation of the a circle passing through (-4, -4) and tangent to the line 2x - 3y +9=0 at (-3,1)?

1 Answer
George C.
Jan 7, 2016

These conditions are inconsistent.

Explanation:

If the circle has centre (-4, -4) and passes through (-3, 1), then the radius has slope (1-(-4))/(-3-(-4)) = 5, but the line 2x-3y+9=0 has slope 2/3 so is not perpendicular to the radius. So the circle is not tangential to the line at that point.

graph{((x+4)^2+(y+4)^2-0.02)((x+4)^2+(y+4)^2-26)(2x-3y+9) = 0 [-22, 18, -10.88, 9.12]}

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