## anonymous 5 years ago Its distance from (0,0) is three times its distance from (4,0)

1. King

3,1

2. anonymous

How?

3. King

see acc. to this x=3y so if x=3 then y =1

4. anonymous

How did you get that answer? Distance formula etc

5. amistre64

id also suggest 3,0

6. amistre64

|dw:1326979014858:dw|

7. nikvist

$x^2+y^2=(3d)^2\quad,\quad (x-4)^2+y^2=d^2$$x^2+y^2=9[(x-4)^2+y^2]$$x^2+y^2=9x^2-72x+144+9y^2$$0=8x^2-72x+144+8y^2$$0=x^2-9x+18+y^2$$0=x^2-9x+20.25-2.25+y^2$$1.5^2=(x-4.5)^2+y^2$$\mbox{all points on circle: }\quad 1.5^2=(x-4.5)^2+y^2$

8. mathmate

or, for the points (0,0) and (x0,y0), all points on the circle $(x-\frac{9x_0}{8})^2+(y-\frac{9y_0}{8})^2 = \frac{9}{64}(x_0^2+y_0^2)$ and for x0=4, y0=0, it reduces to the equation given by nikvist above. Note that both (3,0) and (6,0) satisfy this question's requirements.