Directrix of Parabola – Equation and Formula

Here you will learn formula for finding the equation of directrix of parabola with examples.

Let’s begin –

Equation of Directrix of Parabola

(i) For Parabola \(y^2\) = 4ax :

The equation of directrix is x = -a.

(ii) For Parabola \(y^2\) = -4ax :

The equation of directrix is x = a.

(iii) For Parabola \(x^2\) = 4ay :

The equation of directrix is y = -a

(iv) For Parabola \(x^2\) = -4ay :

The equation of directrix is y = a.

(v) For Parabola \((y – k)^2\) = 4a(x – h) :

The equation of directrix is x + a – h = 0.

(vi) For Parabola \((x – p)^2\) = 4a(y – q) :

The equation of directrix is y + a – q = 0.

Also Read : Different Types of Parabola Equations

Example : For the given parabola, find the equation of the directrices :

(i) \(y^2\) = 8x

(ii) \(x^2\) = -16y

Solution :

(i) The given parabola is of the form \(y^2\) = 4ax, where 4a = 8 i.e. a = 2.

Hence, the equation of the directrix is x = -a i.e. x = -2.

(ii) The given parabola is of the form \(x^2\) = -4ay, where 4a = 16 i.e. a = 4.

Hence, the equation of the directrix is y = a i.e. y = 4.

Example : Find the equation of directrix of the parabola \(y^2 – 8y – x + 19\) = 0

Solution : The given equation is

\(y^2 – 8y – x + 19\) = 0  \(\implies\)  \(y^2 – 8y\) = x – 19

\(\implies\)  \(y^2 – 8y + 16\) = x – 19 + 16

\(\implies\)  \((y – 4)^2\) = (x – 3)

The equation is of the form \((y – k)^2\) = 4a(x – h),

On Comparing we get,

4a = 1 i.e. a = 1/4 and k = 4, h = 3

Hence, the equation of directrix is x + a – h = 0

i.e.  x + (1/4) – 3 = 0 \(\implies\) x = \(11\over 4\)

Leave a Comment

Your email address will not be published.