If parabola y2 = 4kx passes through point (-2, 1), then the length of latus rectum is:

Concept:

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

Calculations:

Given, the parabola y2 = 4kx passes through point (-2, 1),

⇒The  point (-2, 1) is satisfying the equation of parabola y2 = 4kx 

⇒ (1)² = 4k (-2)

⇒ k = \(\rm \dfrac {-1}8\)

Now, the length of the latus rectum = 4k

⇒The length of latus rectum = 4(\(\rm \frac {-1}8\))

⇒The length of latus rectum = \(\frac {-1}{2}\)

The length of latus rectum can not be negative.

⇒The length of latus rectum = \(\frac {1}{2}\)

Hence, if parabola y2 = 4kx passes through the point (-2, 1), then the length of the latus rectum is \(\frac {1}{2}\).