Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let M and N be the number of points on the curve y 5 - 9xy + 2x = 0, where the tangents to the curve are parallel to x-axis and y-axis, respectively. Then the value of M + N equals________.
Text Solution
Verified by ExpertsThe correct answer is:
2
(2)
y 5 - 9xy + 2x = 0
(for horizontal tangent)
Which does not satisfy the original
equation 
M = 0.
Now 5y 4 - 9x = 0 (for vertical tangent)
5y 4 (9y-2)-9y 5 = 0
y 4 [45y-10-9y] = 0
y = 0 (Or) 36y = 10
y = 0 
x = 0&y = 
x =
(0,0) 
N = 2
M+N=0+2=2
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