The tangent at the point P(x₁, y₁) to the parabola y² = 4ax meets the parabola y² = 4a(x + b) at Q and R, the coordinates of the mid-point of QR are

The correct answer is: (x₁, y₁)

Equation of the tangents at P(x₁, y₁) to the parabola y² = 4ax is yy₁ = 2a(x + x₁)
or 2ax – y₁y + 2ax₁ = 0 ….(i)
If M(h, k) is the mid-point of QR, then equation of QR a chord of the parabola y² = 4a(x + b) in term of its mid-point is ky – 2a (x + h) – 4ab = k² – 4a (h + b) (using T = S')
or 2ax – ky + k² – 2ah = 0 …...(ii)
Since (i) and (ii) represent the same line, we have
= =
k = y₁ and k² – 2ah = 2ax₁
– 2ah = 2ax₁  4ax₁ – 2ax₁ = 2ah
h = x₁