Question

\(\sqrt{(x+3)^2+(y-2)^2}=\sqrt{(x-3)^2+y^2}\)
In the xy plane, the set of points whose coordinates satisfy the equation above is??
1) A line
2) A circle
3) An ellipse
4) A parabola
5) One branch of a hyperbola
Please, help

Answer 1

Notice the distance formulas on left and right hand sides, the given equation is same as :

```
distance between (x,y) and (-3, 2) = distance between (x, y) and (3, 0)
```

Answer 2

so you need to find the locus of points that stay at same distance from two points : (-3, 2) and (3, 0)

Answer 3

Thats exactly the definition of perpendicular bisector!

Answer 4

Got you, thank you so much.

Answer 5

Damn!! They are distance formulas!! how can I not see it!!

Answer 6

Haha solving them is fun too, square both sides and all quadratic terms cancel out.. gives the equation of perpendicular bisector..

Answer 7

I did that way but stop at square both sides and look at the square of x and y, I think there must be other way to find the answer out quickly. So that I stopped and post the question. hehehe... I got it from you. Thank you so much

Answer 8

np