ANSWER: ( 4 , - 2 )
We know that ,
The tangency condition of parabola is
c = a/m
Given line → x + y - 2 = 0
Here c = - 2 and m = -1
Parabola → x2 = - 8y
a = 2
a/m = 2/-1 = -2
Hence c = a/m
\(\therefore\) x + y - 2 = 0 is a tangent to the parabola x2 = - 8y .
The equation of tangent at point ( x1 , y1 ) to the parabola x2 = - 8y is
xx1 = -4( y + y1 )
xx1 = -4y - 4y1
xx1 + 4y + 4y1 = 0
comparing the above equation with x + y - 2 = 0
x1 = 4 = - 2y1
x1 = 4
y1 = - 2
\(\therefore\) The coordinates point of contact are ( 4 , - 2 ).