The locus of a point (x, y) whose distance fr | vedclass

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Question

(A) Let the point be $P(x, y)$.The distance between $P(x, y)$ and $(-g, -f)$ is given as $a$.Using the distance formula: $\sqrt{(x - (-g))^2 + (y - (-

Vedclass · Accepted Answer

$x^2 + y^2 + 2gx + 2fy + k = 0$

Vedclass · Answer

(A) Let the point be $P(x, y)$.The distance between $P(x, y)$ and $(-g, -f)$ is given as $a$.Using the distance formula: $\sqrt{(x - (-g))^2 + (y - (-f))^2} = a$Squaring both sides: $(x + g)^2 + (y + f)^2 = a^2$Expanding the squares: $x^2 + 2gx + g^2 + y^2 + 2fy + f^2 = a^2$Rearranging the terms: $x^2 + y^2 + 2gx + 2fy + g^2 + f^2 - a^2 = 0$Given that $k = g^2 + f^2 - a^2$,we substitute $k$ into the equation:$x^2 + y^2 + 2gx + 2fy + k = 0$.

The locus of a point $(x, y)$ whose distance from the point $(-g, -f)$ is always $a$,where $k = g^2 + f^2 - a^2$,is:

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