Parabola
Parabola
nta_abhyas_2025
Grade 11
Question:
Any point on $y = x - 1$ can be taken as $(h, h-1)$. Taking $(h, h-1)$ as the midpoint of chord of $y(h - 1) = 4(\frac{x+1}{2})^2 = (h - 1)^2 - 4bh$, which passes through the point $(h, -2b)$.
Length of latus rectum is less than 4
Length of latus rectum is equal to 4
Length of latus rectum is greater than 4
Cannot be determined
Step-by-Step Solution
Key Concept: The latus rectum length is determined by analyzing the discriminant of the chord equation passing through a fixed point.
The chord equation $b^2 - 2b + (2b' - 2b + 1) = 0$ shows the above equation has two real roots. The discriminant condition $(−2)^2 − 4(1)(2b' − 2b + 1) > 0$ gives $2b' − 2b − c > 0 − c − 1 < 4b < 4$, meaning the length of latus rectum is less than 4.
Correct Answer: 1