y? =4x,
Focus (1, 0),
X=- 1
∴ The distance from P to directrix F is the distance from P to F.
D = distance from p to f+distance from p to l >; = the distance from f to l,
At this time, p is on the vertical line from f to l.
l:4x-3y+6=0,
The slope is 4/3,
The slope of PF is -3/4.
F( 1,0),
Then PF:
y=-(3/4)(x- 1)
Substitute y=-3(x- 1)/4 into the parabola.
9(x- 1)? / 16=4x
arrange
9x? -82x+9=(9x- 1)(x-9)=0,
X=9 or x= 1/9.
P is on the vertical line segment,
Then x < 1, that is, x= 1/9,
y=-(3/4)(x- 1)=2/3,
∴P( 1/9,2/3)