Equation of the locus questions (1 Viewer)

[reggie7]

Hello,

My class is currently finishing off the Prelim course with Locus and the parabola.

Here are 2 questions I can't seem to work out. I get close to the answer in the back of the book. Since the back of the book doesn't have working out I wanna see how someone else gets the final answer.

Question 1. Find the equation of the locus of a point P that moves so that PA is twice the distance of PB where A = (0,3) and B = (4,7)

Question 2. Find the equation of the locus of point P (x,y) that moves so that the ratio of PA to PB is 3:2 where A = (-6, 5) and B = (3, -1)

Answers in BOB:
1. 3x^2 - 32x + 3y^2 - 50y + 251 = 0
2. 5x^2 - 102x + 5y^2 + 58y - 154 = 0

Thanks.

 

[shaon0]

Hello,

My class is currently finishing off the Prelim course with Locus and the parabola.

Here are 2 questions I can't seem to work out. I get close to the answer in the back of the book. Since the back of the book doesn't have working out I wanna see how someone else gets the final answer.

Question 1. Find the equation of the locus of a point P that moves so that PA is twice the distance of PB where A = (0,3) and B = (4,7)

Question 2. Find the equation of the locus of point P (x,y) that moves so that the ratio of PA to PB is 3:2 where A = (-6, 5) and B = (3, -1)

Answers in BOB:
1. 3x^2 - 32x + 3y^2 - 50y + 251 = 0
2. 5x^2 - 102x + 5y^2 + 58y - 154 = 0

Thanks.

1. sqrt((x)^2+(y-3)^2)=2.sqrt((x-4)^2+(y-7)^2)) [since the distance in 2:1 ratio, use the distance formula]
x^2+y^2-6y+9=4x^2-32x+64+4y^2-56y+196
3x^2 - 32x + 3y^2 - 50y + 251 = 0
Complete the square from here on to get the locus as a circle.

2. Follow the same procedure has in the above question.