Coordinate Geometry
Parallel lines from general conic — square of distance
MJAT_TS8_P2
Grade 12
Question:
If $x^2+ay^2+4xy+(2b+1)x+30y+50=0$ represents a pair of parallel lines, then the square of the distance between them is:
Step-by-Step Solution
Key Concept: For parallel lines: $h^2=ab$ where $h=2$ (coefficient of $xy$ is $2h=4$), so $4=a\cdot 1\Rightarrow a=4$. Lines form $(y-mx-C_1)(y-mx-C_2)=0$ with $m=1/2$.
Square of distance $=\mathbf{5}$.
Correct Answer: 5