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
Jan 7, 2016

Answer:

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]}