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 \(r \text{ cm}\).

 
\(A(2,-3 ); \, r=6\)
 

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