Vertex and focus of a parabola are (-1,1) and (2,3) respectively . Find the equation of the directrix . (Please solve it by using foot of the perpendicular) Share with your friends Share 16 Neha Sethi answered this Dear student, In a parabola, vertex is the mid-point of the focus and the point of intersection of the axis and directrix.So, let x,y be the coordinates of the point of intersection of the axis and directrix. Then -1,1 is the mid-pointof the line segment joining 2,3 and x,y.∴x+22=-1 and y+32=1⇒x=-4 and y=-1Thus, the directix meets the axis at -4,-1Let A be the vertex and S be the focus of the required parabola.Then,m1=slope of AS=3-12+1=23Let m2 be the slope of the directrix. Then,m1m2=-1⇒m2=-1m1=-32Thus, the directrix passes through -4,-1 and has slope -32.Therefore, the equation of the directrix is y+1=-32x+4⇒2y+2=-3x-12⇒3x+2y+14=0 Regards 56 View Full Answer Jegannathan Anandaraman answered this Hello Rocky dear, so VF = 5 (by distance formula V(-1,1) and F(2,3) So VM is also 5 units As V is mid point between F and M, M can be found as (-4,-1) Now equation of line joining V and F i.e axis of parabola is y-1 /(1-3) = x +1/(-1-2) Or 2 x - 3 y + 5 = 0 The equation of directrix which is perpendicular to axis can be 3x + 2y + k = 0 As it passes through M, plugging x = -4 and y = -1 we get k = 14 So equation of directrix = 3x + 2y + 14 = 0 7
