## Equation of a Locus that Involves Distance Between Two Points

 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{(x-2)^2+[y-(-3)]^2}&=6 \\\\ (x-2)^2+(y+3)^2&=36 \\\\ x^2-2x+4+y^2+6y+9&=36 \\\\ x^2+y^2-2x+6y-23&=0 . \end{aligned}

## Equation of a Locus that Involves Distance Between Two Points

 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{(x-2)^2+[y-(-3)]^2}&=6 \\\\ (x-2)^2+(y+3)^2&=36 \\\\ x^2-2x+4+y^2+6y+9&=36 \\\\ x^2+y^2-2x+6y-23&=0 . \end{aligned}