Find the locus of a point which is at a distance of 5 units from (-1 , -2)

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Solution

Let, P(x, y) be any point on locus and the given point be A(-1, -2)
Given that, AP = 5 units
i.e. $\sqrt{(x - (- 1))^{2} + (y - (- 2))^{2}} = 5$
$\Rightarrow \sqrt{(x + 1)^{2} + (y + 2)^{2}} = 5$
$\Rightarrow x^{2} + 2 x + 1 + y^{2} + 4 y + 4 = 5$
$\Rightarrow x^{2} + y^{2} + 2 x + 4 y = 0$
$∴$ The required locus is $x^{2} + y^{2} + 2 x + 4 y = 0$

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