7.4 
Equation of a Locus that Involves Distance Between Two Points


Locus of a point \(P(x, \,y)\) is the path travelled by the point which moves under a given condition.
The equation of a locus involving the distance between two points can be determined by using the distance formula.


Example:
Find the equation of the locus of a moving point \(P(x,y)\) such that its distance from a fixed point \(A\) is \(r \text{ cm}\).


\(A(2,3 ); \, r=6\) 

\(\begin{aligned} AP&=6 \\\\ \sqrt{(x2)^2+[y(3)]^2}&=6 \\\\ (x2)^2+(y+3)^2&=36 \\\\ x^22x+4+y^2+6y+9&=36 \\\\ x^2+y^22x+6y23&=0 . \end{aligned}\)