Here equation of curve is y5−9xy+2x=0..... (i) On differentiating: 5y4
dy
dx
−9y−9x
dy
dx
+2=0 ∴
dy
dx
=
9y−2
5y4−9x
When tangents are parallel to x-axis then 9y−2=0 ∴M=1. For tangent perpendicular to x-axis 5y4−9x=0...... (ii) From equation (i) and (ii) we get only one point. ∴N=1. ∴M+N=2