The equation of the directrix of the parabola whose vertex and focus are (1,4) and (2,6) respectively is `x+2y=4` b. `x-y=3` c. `2x+y=5` d. `x+3y=8`

Options

A. x+2y=4
B. x-y=3
C. 2x+y=5
D. x+3y=8

Answer

A

Explanation

The equation of the axis of the parabola is
`y-4=(6-4)/(2-1)(x-1)or, 2x-y+2=0`
Let `(x_(1), x_(1))` be the point of intersection of axis and directrix. Since vertex is the mid-point of `(x_(1), x_(1))` abd focus of the parabola.
`1=(x_(1)+2)/2" and "4=(y_(1)+6)/2rArrx_(1)=0" and "y_(1)=2`
Clearly, directrix passes through `(x_(1), y_(1))=(0, 2)` and is perpendicular to axis. So, its equation is
`y-2-1/2(x-0)or x+2y-4=0`