Find the equation of the chord of contact AB of tangents drawn from an external point $(X1,Y1)$ to the parabola $X^2=-36y$

Question

Q: Find the equation of the chord of contact AB of tangents drawn from an external point $(X1,Y1)$ to the parabola $X^2=-36y$

My working:

Let $A(2aA,aA^2), B(2aB, aB^2)$

-> Equation of chord AB $ y=\frac{A+B}{2}x-aAB$

-> Point of tangent intersection $[a(A+B), aAB]$

--> $X1=a(A+B)$

--> $Y1=aAB$

---> $y=\frac{X1x}{2a} - Y1$ since a=9

-> Equation: $18(y+Y1)=X1x$

-> However the answer is $-18(y+Y1)=X1x$

What am I doing wrong, is a allowed to be negative?