Question

If parabola y² = px passes through point (-2, 3), then the length of latus rectum is:

1. 18
2. 9
3. 4.5
4. 3

Answer 1

Correct Answer - Option 3 : 4.5

Concept:

The length of the latus rectum of the parabola y² = 4ax is 4a.

 

Calculation:

Since the point (-2, 3) is on the parabola y2 = px, we must have:

(3)2 = p(-2)

⇒ p = -4.5

Comparing this with the standard equation y2 = 4ax, we can say that the length of the latus rectum is 4a = p.

As we know, length cannot be negative so the length of latus rectum = 4a = |p| = 4.5