I need help because I got stuck on this problem :
Find the equation of the locus of a point P = (x,y) that moves in accordance with each of the following conditions, and sketch the graphs:
a. The sum of the squares of the distances from P to the points (a,0) and (-a,0) is 4b^2, where b >= a/sqrt of 2 > 0
b. the distance of P from the point (8,0) is twice its distance from the point (0,4).
what ive done so far :
I think B is a line between the points (0,4) and (8,0) with a slope of 2/1. 2/1 is the negative reciprical of the line that goes threw (0,4) and (8,0)
So y=2X+B is the line I get for P according to the second guideline (b.).
Y and x of the point P must both work out to this formula so I should be able to substitute y for 2x+B in the equation I get from Part a of this problem. :
10x^2+2a^2+8xb-2b^2 = 0
Now I have the equation of some point I guess. But I dont know how to solve it from here. All I can think to do is simplify it all by dividing by 2. but then I get stuck. Someone please help.
The distance from P to B(0,4) is:
2. According to the question you'll get:
3. Expand the brackets, collect like terms and afterwards complete the squares.
4. For further informations have a look here: Circles of Apollonius - Wikipedia, the free encyclopedia