If the focus of the parabola is -2 -1 and the equation of directrix is x+y = 3

IMG_20190305_112758.jpg

Sr plz solve it If the focus of the parabola is (-2,-1) and the equation of directrix is x+y=3. Then the coordinates of vertex are:

Answers (1)

H himanshu.meshram

@Mannika

Focus of parabola is (-2,-1)

equation of Directrix = x + y = 3

vertex of the parabola is the mid-point of the line segment joining the focus to the intersection point of the axis and directrix

The equation of the axis is $x-y=\lambda\: \: i.e.\: \: -2-(-1)=\lambda \Rightarrow \lambda = -1$

as axis is perpendicular to directrix and axis is passing via (-2, -1)

$x-y+1=0$

Point D is the intersection of Directrix and Axis (1, 2)

Thus V can be calculated

V is the midpoint of S and D

Let (h , k) be vertex.

Then

$\\h=\frac{-2+1}{2}\:\:,\:\:k=\frac{-1+2}{2}\\(h,k)=(\frac{-1}{2},\frac{1}{2})$