SOLUTION: A point P moves such that it is always twice as far from the points (4,0) as it is on the line x = 1 a) find the equation of the locus b) identify the locus and graph Thanks v

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A point P moves such that it is always twice as far from the points (4,0) as it is on the line x = 1 a) find the equation of the locus b) identify the locus and graph Thanks v      Log On


   

Question 824655: A point P moves such that it is always twice as far from the points (4,0) as it is on the line x = 1
a) find the equation of the locus
b) identify the locus and graph
Thanks very much in advance:)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28%28x-4%29%5E2%2B%28y%29%5E2%29
sqrt%28x%5E2-8x%2B16%2By%5E2%29, distance to given point


sqrt%28%28x-1%29%5E2%2B%28y-y%29%5E2%29
sqrt%28x%5E2-2x%2B1%29,distance to given line


sqrt%28x%5E2-8x%2B16%2By%5E2%29=2%2Asqrt%28x%5E2-2x%2B1%29, according to description
x%5E2-8x%2B16%2By%5E2=4x%5E2-8x%2B4
16%2By%5E2=3x%5E2%2B4
12%2By%5E2=3x%5E2
3x%5E2-y%5E2=12
highlight%28x%5E2%2F4-y%5E2%2F12=1%29