If the locus of the point, whose distances from the point $(2,1)$ and $(1,3)$ are in the ratio $5: 4$, is $a x^2+b y^2+c x y+d x+e y+170=0$, then the value of $a^2+2 b+3 c+4 d+e$ is equal to :

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Aicharya · Accepted Answer

let $\mathrm{P}(\mathrm{x}, \mathrm{y})$ $\begin{aligned} & \frac{(x-2)^2+(y-1)^2}{(x-1)^2+(y-3)^2}=\frac{25}{16} \ & 9 x^2+9 y^2+14 x-118 y+170=0 \ & a^2+2 b+3 c+4 d+e \ & =81+18+0+56-118 \ & =155-118 \ & =37 \end{aligned}$

If the locus of the point, whose distances from the point $(2,1)$ and $(1,3)$ are in the ratio $5: 4$, is $a…

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