Question

consider the following.
find an equation of the parabola.
find the focus and directrix.
focus $(x,y)=$
directrix
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Explanation:

Step1: Determine the standard form of the parabola

Since the parabola opens to the left, its standard form is \(y^{2}=4px\), where \(p<0\).

Step2: Find the value of \(p\)

From the graph, when \(y = 1\), \(x=-\frac{1}{4}\). Substitute \(x =-\frac{1}{4}\) and \(y = 1\) into \(y^{2}=4px\):

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Step3: Write the equation of the parabola

Substitute \(p=-1\) into \(y^{2}=4px\), we get \(y^{2}=-4x\).

Step4: Find the focus

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

Step5: Find the directrix

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

Answer:

• Equation of the parabola: \(y^{2}=-4x\)
• Focus: \((x,y)=(-1,0)\)
• Directrix: \(x = 1\)