Answer:-
P(ap2,2ap),Q(aq2,2aq)y2=4ax
The tangents is
y⋅y0=2a(x+x0)
PR:
y⋅2ap=2a(x+ap2)x−py+ap2=0
QR:
y⋅2aq=2a(x+aq2)x−qy+aq2=0
R=PR∩ QR
x−py+ap2=0x−qy+aq2=0y=q−pa(p2−q2)=a(p+q)x=aqpR(aqp,a(p+q))
OQ:
aq2−0x−0=2aq−0y−0y=q2xkOQ=q2
OQ⊥ RP
kRP=−kOQ1=−2q
RP:
y=p1x+apkRP=p1p1=−2qpq=−2
multiply by a
apq=−2ax=−2ax+2a=0
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