Parabola
Chord Through Two Points and Centroid of Triangle
nta_pyq_2023_apr
Grade 11
Question:
Let $R$ be the focus of $y^2=20x$ and the line $y=mx+c$ intersect the parabola at $P$ and $Q$. Let $G(10,10)$ be the centroid of $\triangle PQR$. If $c-m=6$, then $(PQ)^2$ is
Step-by-Step Solution
Key Concept: Parametric points on $y^2=20x$: $(5t^2,10t)$. Focus $R=(5,0)$. From centroid conditions: $t_1^2+t_2^2=5$ and $t_1+t_2=3$.
$P=(5,10),Q=(20,20)$. $(PQ)^2=325$.
Correct Answer: 2