AMU Engineering 2020 solved paper Solved Paper

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