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Question

If Ax+By=1 is a normal to the curve ay=x2 , then 
  1. 4A2(1aB)=aB3
  2. 4A2(1+aB)+aB3=0
  3. 2A2(2aB)=aB3
  4. 4A2(2+aB)=aB3


Solution

The correct option is C 2A2(2aB)=aB3
Ax+By=1
y=ABx+1B   (i) 
This is a normal to the parabola x2=ay 
We know that, the equation of normal to parabola x2=4by is 
y=mx+2b+bm2
For the given curve b=a4
Then, equation of normal is
y=mx+a2+a4m2   (ii)

Comparing (ii) with the given line (i), we get
m=AB1B=a2+a4m21Ba2=aB24A2(2aB)2A2=aB3

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