Parabola y² = 4ax
Conic Sections · Class XI
Slide the parameter a , the parabola opens right (a > 0) or left (a < 0).
- Focus1
- Directrix x-1
- Latus rectum length4
- Upper branch y = +√(4ax)
- Lower branch y = −√(4ax)
Formulas in this lab
- Focus
- Directrix x
- Latus rectum length
Frequently asked questions
▶What is the standard equation of a parabola?
The parabola $y^2 = 4ax$ opens to the right with focus at $(a, 0)$ and directrix $x = -a$. Every point on it is equidistant from the focus and the directrix. The latus rectum has length $4a$, a quick JEE memory hook.
▶How do I use the parabola explorer lab?
Slide the focal parameter $a$. The lab plots $y^2 = 4ax$ and marks the focus and directrix live. Set $a = 2$: the focus sits at $(2, 0)$, the directrix is $x = -2$ and the latus rectum is $8$ units long.
▶Where do parabolas show up in engineering?
Satellite dish antennas (like those for Tata Play) and car headlight reflectors are paraboloids of revolution — rays parallel to the axis focus at one point. The projectile trajectory of a thrown cricket ball is also a parabola. The lab gives you a tactile feel for the focal property.
▶Common JEE pitfall: $y^2 = 4ax$ versus $y = ax^2$
$y^2 = 4ax$ opens sideways; $y = ax^2$ opens upward. Both are parabolas but with different orientations and focus formulas. Students plug into the wrong formula and lose easy marks. The lab here is for the horizontal form; sketch $y = ax^2$ separately to compare.