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virtus
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.
Lets call that point P (x, y)
distance from (-1, 3) to P(x, y) is always 5
you know the distance formula ?
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
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.
can you tell... what shape it can be ?
THANK YOU SO MUCH GANESHIE8 ! =D