find the equation of the locus of the point P(x,y) that moves so that the ratio of PA to PB is 3:2 with points A(-6,5) and B (3, -1)
Answers
Given : point P(x,y) that moves so that the ratio of PA to PB is 3:2 with points A(-6,5) and B (3, -1)
To Find : locus of the point P(x,y)
Solution:
P ( x , y)
A ( - 6 , 5)
B ( 3 , -1 )
PA² = ( x+6)² + ( y - 5)²
PB² = ( x - 3)² + ( y + 1)²
PA : PB = 3 : 2
=> PA² : PB² = 9 : 4
=> 4 PA² = 9 PB²
=> 4 ( ( x+6)² + ( y - 5)² ) = 9 ( ( x - 3)² + ( y + 1)²)
=> 4(x² + 12x + 36 + y² - 10y + 25) = 9 ( x² -6x + 9 + y² +2y + 1)
=> 4x² + 48x + 4y² - 40y + 244 = 9x² -54x + 9y² + 18y + 90
=> 5x² + 5y² - 102x +58y - 154 = 0
5x² + 5y² - 102x +58y - 154 = 0 is locus of the point P(x,y)
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