The equation of the tangent y2=8x at P(2,4) is 4y=4(x+2) ⇒‌‌‌‌x−y+2=0 . . . (i) Let (x1,y1) be the mid-point of chord QR. Then, equation of QR is yy1−4(x+x1)−5=y12−8x1−5 ⇒‌‌4x−yy1−4x1+y12=0 . . . (ii) Clearly, Eqs. (i) and (ii) represent the same line. ∴‌‌‌
4
1
=‌
−y1
−1
=‌
−4x1+y12
2
⇒‌‌‌‌y1=4‌ and ‌8=−4x1,+y12 ⇒‌‌‌‌y1=4‌ and ‌x1=2