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Determine the focus coordinates, the axis of the parabola, the equation of the directrix and the latus rectum length for y 2 = -8x

Determine the focus coordinates, the axis of the parabola, the equation of the directrix and the latus rectum length for y2 = -8x

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5965 Points
one year ago
Welcome to AskIITians

Given that, the parabola equation is y2= -8x.

It is noted that the coefficient of x is negative.

Therefore, the parabola opens towards the left.

Now, compare the equation with y2= -4ax, we obtain

-4a= -8

⇒ a = 2

Thus, the value of a is 2.

Therefore, the coordinates of the focus = (-a, 0) = (-2, 0)

Since the given equation involves y2, the axis of the parabola is the x-axis.

Equation of directrix, x= a i.e., x = 2

We know the formula to find the length of a latus rectum

Latus rectum length= 4a

Now, substitute a = 2, we get

Length of latus rectum = 8

Thanks

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