Let ... x² + y² + 2gx + 2fy + c = 0 ... (1)
and ... y² = 4ax, a > 0 .................... (2)
From (2), ... x = y² / (4a).
Putting this value of x in (1), we get
( y⁴ / 16a²) + y² + 2g(y² / 2a) + 2fy + c = 0
∴ y⁴ + 0y³ + (16a²+8ag)y² + (32a²f)y + 16a²c = 0 ......... (3)
This equation gives the Ordinates of the 4 points of intersection
of the circle and the parabola.
Sum of These Ordinates
= Sum of Roots of eq(3)
= (-1)* { ( coeff. of y³ ) / ( coeff. of y⁴ )} [using Vieta's Relation]
= - ( 0 / 1 )
= 0.