What is the locus of the moving point p ((7t-2)/(3t+2) ,(4t+5)/(t-1))?

analianopolisca

analianopolisca

Answered question

2022-08-07

What is the locus of the moving point p ((7t-2)/(3t+2) ,(4t+5)/(t-1))?

Answer & Explanation

Kelsie Marks

Kelsie Marks

Beginner2022-08-08Added 17 answers

x = 7 t 2 3 t + 2 , y = 4 t + 5 t 1
3 x t + 2 x = 7 t 2
3 x t 7 t = 2 x 2
t ( 3 x 7 ) = 2 x 2
t = 2 x + 2 7 3 x ....(1)
yt - y = 4t + 5
y t 4 t = y + 5
t ( y 4 ) = y + 5
t = y + 5 y 4 ....(2)
y + 5 y 4 = 2 x + 2 7 3 x
7 y 3 x y + 35 15 x = 2 x y 8 x 8 + 2 y
5 x y + 7 x 5 y 43 = 0
so, the locus of the given point p is 5 x y + 7 x - 5y-43=0

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