Two parabola have the same focus. If their directrices are the x-axis and the y-axis respectively, then the slope of their common chord is :

Options

A. -1
B. `-1//2`
C. `-sqrt(3)//2`
D. none of these

Answer

A

Explanation

(1) Let the focus be F. The parabola are open-down and open-right, respectively.
Let the parabolas intersect at point P and Q. From P, perpendiculars are drawn on the x-and the y-axis at A and B, respectively, Then,
PA=PF=PB
So, P lies on the line =-x.
Similarly, Q lies on the y=-x. Therefore, Slope of PQ =-1