The correct options are
B m=−√2
C m=√2
Making y2=4ax homogeneous with the help of
y=mx−2am−am3
or mx−y=2am+am3
or mx−y2am+am3=1
then y2=4ax×(1)
y2=4ax×(mx−y2am+am3)
y2=4x(mx−y)(2m+m2)
⇒(2m+m2)y2−4mx2+4xy=0 ........(1)
∵ angle between the lines represented by eqn(1) is π2 (given)
∴ coefficient of x2+coefficient of x2=0
⇒−4m+(2m+m3)=0
⇒m3−2m=0
⇒m(m2−2)=0
⇒m≠0,m2=2
∴m=±√2