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 + ey + 170 = 0 , then the value of a 2 + 2 b + 3 c + 4 d + e i

Question

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 + ey + 170 = 0 , then the value of a 2 + 2 b + 3 c + 4 d + e is equal to :

TestHub · Accepted Answer

let P ( x , y ) ​ ( x − 1 ) 2 + ( y − 3 ) 2 ( x − 2 ) 2 + ( y − 1 ) 2 ​ = 16 25 ​ 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 ​

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