Parabola..

The equation of the normal at the point (m², 2m) is
y = mx -2m -m³
If this normal passes through A(h,k) then
k = mh -2m -m³ i.e. m³ +(2-h) m +k =0
This being a cubic in m gives three values of m, say m₁, m₂, m₃ which would give the three points P(m₁² , 2m₁), Q(m₂² , 2m₂), and R(m₃² , 2m₃), the normals at which intersect in A.
We have,
m₁ + m₂ + m₃ = 0
m₁m₂ + m₂m₃ + m₃m₁ = 2-h
m₁m₂m₃ = -k

Then,
SP . SQ . SR = (1+m₁²)(1+m₂²)(1+m₃²)
= 1 + m₁² + m₂² + m₃² + m₁²m₂² + m₂²m₃² + m₃²m₁² + m₁²m₂²m₃²

But
m₁² + m₂² + m₃² = (m₁ + m₂ + m₃)² - 2(m₁m₂ + m₂m₃ + m₃m₁ ) = 2(h-2)

And
m₁²m₂² + m₂²m₃² + m₃²m₁² = (m₁m₂ + m₂m₃ + m₃m₁ )² - 2m₁m₂m₃(m₁ + m₂ + m₃)
=(2-h)²

Plugging back, we get
SP . SQ . SR = 1 + 2(h-2) + (2-h)² + k² = (1+h-2)²+k² = (h-1)²+k² = SA²

Hence, \alpha = 1