Question

The maximum number of normals which can be drawn common to y2 = 4ax and x2 = 4 by is?​

Answer 1

Answer:

Step-by-step explanation:

Equation of normal to the curve y  

2

=4ax and x  

2

=4by in terms of m are given by

y=mx−2am−am  

3

 and y=mx+2b+  

m  

2

 

b

​  

 

For common normals both values of y are equal

∴2b+  

m  

2

 

b

​  

+2am+am  

3

=0

⇒am  

5

+2am  

3

+2bm  

2

+b=0

which can attain maximum 5 values of m

so maximum normals can be 5