if the vertics and the focous of the parabola are (-1,1)and (2,3) respectively,then equation of its directrix is

since the vertex of the parabola is the mid point of of the line joining the focal point and point on the directrix .therefore  let the point on the directrix be (x1,y1).

vertex is (-1,1)and focus is (2,3) take out the point on directrix by mid point formula . its (-4,-1)

now the slope of line joining vertex and focus is 3-1/2+1=2/3=m1; (slope formula)

since directrix is perpendicular to th line jopining vertex and focus ;by slpoe of perpendicular lines- m1*m2=-1

m2=-3/2(slope of the directrix)

put this in sliope point form

point is (-4,-1) and slope= -3/2

eq. is y+1=-3/2(x+4)

solve it!!hope it works!!!!

the vertices is the mid pt. of focus and directrix.let coordinates of dirextrix be(x,y)

so,-1=x+2/2

=-2=x+2

x=-4

1=y+3/2

=2=y+3

y=-1

using slope formula

the slope of line joining vertex and focus is 3-1/2+1=2/3=m1

directrix is perpendicular to th line jopining vertex and focus ;by slpoe of perpendicular lines- m1 x m2=-1

m2=-3/2

put in point slope form

eq. is y+1=-3/2(x+4)

find the eqn