Question

question is here it is a maths question plz ans mi​

Answer 1

Answer:

hey here is your answer

pls mark it as brainliest

Step-by-step explanation:

$to \: find = \\ equation \: of \: locus \: of \: point \: P \\ \\ so \: here \: as \: point \: P \: is \: a \: locus \\ points \: M \: and \: N \: must \: be \: equidistant \: from \: it \\ ie \: PM = PN \\ \\ so \: here \: \\ M = (3, - 1) \\ N = (2,3) \\ P = (x ,y)\\ \\ moreover \: \: \frac{PM}{PN} = \frac{3}{2} \\ \\ ie \: 2.PM = 3.PN \\ squaring \: both \: sides \\ we \: get \\ 4.PM {}^{2} = 9.PN {}^{2}$

$hence \: then \\ 4((x - 3) {}^{2} + (y - ( - 1)) {}^{2} ) = 9.((x - 2) {}^{2} + (y - 3) {}^{2}) \\ 4.((x - 3) {}^{2} + (y + 1) {}^{2} ) = 9.((x - 2) { }^{2} + (y - 3) {}^{2} ) \\ \\ 4.(x {}^{2} + 9 - 6x + y {}^{2} + 1 + 2y) = 9.(x {}^{2} + 4 - 4x + {y}^{2} + 9 - 6y) \\ 4(x {}^{2} + y {}^{2} - 6x + 2y + 10) = 9.(x {}^{2} + y {}^{2} - 4x - 6y + 13) \\ \\ 4x {}^{2} + 4y {}^{2} - 24x + 8y + 40 = 9x {}^{2} + 9y {}^{2} - 36x - 54y + 117 \\ \: 9x {}^{2} + 9y {}^{2} - 36x - 54y + 117 - (4x {}^{2} + 4y {}^{2} - 24x + 8y + 40) = 0 \\ = (9x {}^{2} - 4x {}^{2} ) + (9y {}^{2} - 4y {}^{2} ) - (36x + 24x) - 54y - 8y + 117 - 40 \\ = 5x {}^{2} + 5y {}^{2} - 12x - 62y + 77 \\ \\ ie \: \: 5x { }^{2} + 5y {}^{2} - 12x - 62y + 77 = 0$