Question

# If Ax+By=1 is a normal to the curve ay=x2 , then 4A2(1−aB)=aB34A2(1+aB)+aB3=02A2(2−aB)=aB34A2(2+aB)=aB3

Solution

## The correct option is C 2A2(2−aB)=aB3Ax+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+a4m2⇒1B−a2=aB24A2∴(2−aB)2A2=aB3

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