Question

Find the equation of the latus rectum of the parabola y² = - 6x ?
1. x = 3/2
2. x = - 3/2
3. y = 3/2
4. y = - 3/2
5. None of these

Answer 1

Correct Answer - Option 2 : x = - 3/2

CONCEPT:

The following are the properties of a parabola of the form: y2 = - 4ax where a > 0

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

CALCULATION:

Given: Equation of the parabola is y2 = - 6x

The given equation of parabola can be re-written as: y2 = - 4 ⋅ (3/2)x      ----(1)

Now by comparing the equation (1) with y2 = - 4ax we get

⇒ a = 3/2

As we know that, equation of latus rectum of the parabola of the form y2 = - 4ax is given by: x = - a

So, equation of latus rectum of given parabola is: x = - 3/2

Hence, option B is the correct answer.