A point P(x, y) moves so that the sum of the squares of its distance from each of the points A(–1, 0) and B(3, 0) is equal to 40. Show that the locus of P(x, y) is a circle, and state its radius and centre. i did PA^2+PB^2=40 after completing the steps im supposed to get
⎡(x + 1)^2 + y2 ⎤⎡(x − 3)^2 + y2 ⎤⎦= 40
⎣⎦ + ⎣ x^2 + 2x + 1 + y^2 + x^2 − 6x + 9 + y^2 = 40
2x^2 − 4x + 2y^2 = 15
i don't understand where the 15 came from ? someone please explain

Question

A point P(x, y) moves so that the sum of the squares of its distance from each of the points A(–1, 0) and B(3, 0) is equal to 40. Show that the locus of P(x, y) is a circle, and state its radius and centre. i did PA^2+PB^2=40 after completing the steps im supposed to get
 ⎡(x + 1)^2 + y2 ⎤⎡(x − 3)^2 + y2 ⎤⎦= 40
⎣⎦ + ⎣ x^2 + 2x + 1 + y^2 + x^2 − 6x + 9 + y^2 = 40 
2x^2 − 4x + 2y^2 = 15
i don't understand where the 15 came from ? someone please explain

anonymous · Answer

i think its x^2 -2x + y^2 = 15

try to check ur answer

anonymous · Answer

yh u can do that too, but dividing 2x^2+2y^2-4x by2 but what i dnt get is where did the 15 come from ?:/

anonymous · Answer

ohh i got it !! nvm they did 30 divide by 2 as well !!

anonymous · Answer

is that the answer given to that problem???

anonymous · Answer

nah there is more to it, the final answer is (x-1)^2+y^2=16
c(1,0) R=4

sirm3d · Answer

$$\large x^2+2x+1+y^2+x^2-6x+9+y^2=40$$$$\large 2x^2-4x+2y^2+10=40$$$$\large 2x^2-4x+2y^2=30$$$$\large x^2-2x+y^2=15$$$$\large x^2-2x+1+y^2=15+1$$$$\large (x-1)^2+(y-0)^2=4^2$$