Question

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.

Answer 1

Lets call that point P (x, y)

Answer 2

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

Answer 3

you know the distance formula ?

Answer 4

yes

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

THANK YOU SO MUCH GANESHIE8 ! =D