Question

find the coordinates of the focus and equation of the directrix for the parabola given by
$y^{2}=-4x$.
the general formula for this parabola is $y^{2}=4px$.
therefore, the value of $p$ is.
the coordinates of the focus are.
the equation of the directrix is.

Explanation:

Step1: Find the value of \(p\)

Compare \(y^{2}=-4x\) with \(y^{2} = 4px\).
We have \(4p=-4\), so \(p=-1\).

Step2: Find the focus coordinates

For a parabola \(y^{2}=4px\), the focus is \((p,0)\).
Since \(p = - 1\), the focus is \((-1,0)\).

Step3: Find the directrix equation

For a parabola \(y^{2}=4px\), the directrix is \(x=-p\).
Since \(p=-1\), the directrix is \(x = 1\).

Answer:

The value of \(p\) is \(-1\). The coordinates of the focus are \((-1,0)\). The equation of the directrix is \(x = 1\).