Parabola
Focal Chord Division — Minimum of α+β
nta_pyq_2026_jan
Grade 11
Question:
Let one end of a focal chord of the parabola $y^2=16x$ be $(16,16)$. If $P(\alpha,\beta)$ divides this focal chord internally in the ratio $5:2$, then the minimum value of $\alpha+\beta$ is equal to:
Step-by-Step Solution
Key Concept: Parabola $y^2=16x$: $a=4$, focus $(4,0)$. Point $(16,16)$ has parameter $t_1=2$. Other end: $t_2=-1/t_1=-1/2$, giving $(1,-4)$. $P$ divides $(16,16)$ to $(1,-4)$ in ratio $5:2$.
Minimum $\alpha+\beta=7$.
Correct Answer: 3