Question

Find the equation of the latus rectum of the parabola x² = -8y ?
1. y = -2
2. y = 2
3. x = -2
4. x = 2
5. None of these

Answer 1

Correct Answer - Option 1 : y = -2

CONCEPT:

The following are the properties of a parabola of the form: x2 = - 4ay where a > 0

• Focus is given by (0, - a)
• Vertex is given by (0, 0)
• Equation of directrix is given by: y = a
• Equation of axis is given by: x = 0
• Length of latus rectum is given by: 4a
• Equation of latus rectum is given by: y = -a

CALCULATION:

Given: Equation of the parabola is x2 = -8y

The given equation of parabola can be re-written as: x2 = - 4 ⋅ 2y      ----(1)

Now by comparing the equation (1) with x2 = -4ay we get

⇒ a = 2

As we know that, equation of latus rectum of the parabola of the form x2 = -4ay is given by: y = -a

So, equation of latus rectum of given parabola is: y = - 2

Hence, option A is the correct answer.