Maximum number of common normals of y^2=4ax and x^2=4by may be equal to

• 2
• 4
• 5
• none of these

Hello student,
Equations of normals to y² = 4ax and x² = 4by are given by
y = mx – 2am – am³
and y = mx + 2b + b/m²
Now, according to the requirement, for common normals, 2b + b/m² + 2am + am³ = 0
This gives am⁵ + 2am³ + 2bm² + b = 0
So, a maximum of 5 normals are possible.
Hence, the correct answer is (c).