The slope of line which belongs to family (1+ l) x + (1-l)y + 2(1-l) = 0 and makes shortest intercept on `x^2 = 4y - 4`

Answer

0

Explanation

0 The family of lines `(1+lamda)x+(lamda-1)y+2(1-lamda)=0` is concurrent at (0,2). The focus of the parabola `x^(2)=4(y-1)` is (0,2).
Now, the shortest intercept of the line on the parabola which passes through the focus is latus rectum.
The axis of the given parabola is the y-axis.
Therefore, the latus rectum is parallel to the x-axis.