UPSC NDA Math Model Paper 10

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=

−1

8

Now, the length of the latus rectum =4k
⇒ The length of latus rectum =4(

−1

8

)
⇒ The length of latus rectum =

−1

2

The length of latus rectum can not be negative.
⇒ The length of latus rectum =

1

2

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

1

2

.