## virtus Group Title find the equation of the locus of a point that moves so that it is always 5 units from (-1,3). Describe the shape of this locus. 2 years ago 2 years ago

1. ganeshie8

Lets call that point P (x, y)

2. ganeshie8

distance from (-1, 3) to P(x, y) is always 5

3. ganeshie8

you know the distance formula ?

4. virtus

yes

5. ganeshie8

Okay good. distance between (-1, 3) and P(x, y) : $$\sqrt{(x2-x1)^2+(y2-y1)^2}$$ = 5 $$\sqrt{(x-(-1))^2+(y-3)^2}$$ = 5 $$\sqrt{(x+1)^2+(y-3)^2}$$ = 5 squating on both sides, $$(x+1)^2+(y-3)^2$$ = 25

6. Ron.mystery

POINTS TO REMEMBER: A locus or curve is the set of points and only those points satisfying a given condition or a well defined property. This is the locus definition in geometry. Example of locus is provided below: (1) A,B are two fixed points. Let a set of points equidistant from A and B. Locus is the perpendicular bisector of AB . Every point on the perpendicular bisector of AB obeys the condition. (2) The locus of a set of points which are at a constant distance from a fixed point,is a circle.

7. ganeshie8

@virtus thats our locus equation.

8. ganeshie8

can you tell... what shape it can be ?

9. virtus

THANK YOU SO MUCH GANESHIE8 ! =D

10. ganeshie8

i dont think, from equation its shape is obvious... we need to know about circle to be able to visualize the shape. np :)