Straight Lines
Locus — Ratio of Distances
nta_pyq_2024_apr
Grade 11
Question:
If the locus of the point, whose distances from the point $(2,1)$ and $(1,3)$ are in the ratio $5:4$, is $ax^2+by^2+cxy+dx+ey+170=0$, then the value of $a^2+2b+3c+4d+e$ is equal to:
Step-by-Step Solution
Key Concept: Let $P=(x,y)$. $\frac{(x-2)^2+(y-1)^2}{(x-1)^2+(y-3)^2}=\frac{25}{16}$. Cross-multiply and expand.
$a=9,b=9,c=0,d=14,e=-118$. $a^2+2b+3c+4d+e=37$.
Correct Answer: 1