If the tangents at the extremities of a focal chord of
the parabola $x^2=4ay$ meet the tangent at the vertex
at points whose abcissac are $x_1$ and $x_2$ then $x_1{x}_2=$

One extremity of the focal chord be $\left(2at,a{t}^2\right)$ . Equation
of the tangent is $tx=y+a{t}^2$ which meets the
tangent at the vertex $y=0$ at $x=at$ so $x_1=at$ and 

$x_2=a\left(-\frac{1}{t}\right)$ thus $x_1{x}_2=-a^2$.