Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. x^2 =

Home » Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. x^2 = – 9y

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. x^2 = – 9y

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. x^2 = – 9y

Given:

The condition is

${{x}^{2}}~=\text{ }-9y$

Here we realize that the coefficient of

$y$

is negative .

Along these lines, the parabola opens towards downwards .

On contrasting this condition and

${{x}^{2}}~=\text{ }-4ay$

, we get,

$\begin{array}{*{35}{l}} 4a\text{ }=\text{ }-9 \\ a\text{ }=\text{ }-9/-4\text{ }=\text{ }9/4 \\ \end{array}$

Accordingly, the co-ordinates of the concentration

$=\text{ }\left( 0,-a \right)\text{ }=\text{ }\left( 0,\text{ }-9/4 \right)$

Since, the given condition includes

${{x}^{2}}$

, the axis of the parabola is the

$y-axis$

.

∴ The condition of directrix,

$y\text{ }=\text{ }a$

, then, at that point,

$y\text{ }=~9/4$

Length of latus rectum

$=\text{ }4a\text{ }=\text{ }4\left( 9/4 \right)\text{ }=\text{ }9$

i

Sign up now and study all subjects for free