Question

If the vertex and the focus of a parabola are (1, 1) and (2, 3) respectively, then the equation of the directrix is

Answer 1

vertex A=(1,1)&

focus S=(2,3)

AS is the principal axis whose slope=

$\frac{3 - 1}{2 - 1} = 2$

since directrix is perpendicular to the principal axis,

slope of the directrix =

$- \frac{1}{2}$

and if Z is the foot of A on directrix

then A becomes the mid point of ZS

so Z=2A-S

Z=(2,2)-(2,3)=(0,-1)

hence equation of the directrix is

$y - ( - 1) = - \frac{1}{2} (x - 0)$

$y + 1 = - \frac{x}{2}$

$2y + 2 = - x$

$x + 2y + 2 = 0$

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