3D Geometry
Line-Plane Intersection — Quadratic with Distance Roots
nta_pyq_2023_apr
Grade 12
Question:
$P$ = intersection of $\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2}$ with $x+y+z=2$. Distance from $P$ to $3x-4y+12z=32$ is $q$. Then $q$ and $2q$ are roots of
x^2-18x-72=0
x^2-18x+72=0
x^2+18x+72=0
x^2+18x-72=0
Step-by-Step Solution
Key Concept: Find $P$ by substituting parametric line into plane. Compute distance $q$. Quadratic with roots $q,2q$.
$x^2-18x+72=0$.
Correct Answer: 2