| 7.4 |
Equation of a Locus that Involves Distance Between Two Points
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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.
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Example:
Find the equation of the locus of a moving point \(P(x,y)\) such that its distance from a fixed point \(A\) is \(r \text{ cm}\).
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| \(A(2,-3 ); \, r=6\) |
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\(\begin{aligned} AP&=6 \\\\ \sqrt{(x-2)^2+[y-(-3)]^2}&=6 \\\\ (x-2)^2+(y+3)^2&=36 \\\\ x^2-2x+4+y^2+6y+9&=36 \\\\ x^2+y^2-2x+6y-23&=0 . \end{aligned}\)
