Can anyone help me with this locus question? (1 Viewer)

MysteryMoon · May 20, 2015

Find the equation of the locus of a point that moves so that it is equidistant from point (2,-3) and line y=7
The answer is x^2 - 4x + 20y -36 = 0

I remember being able to do this before but it's been ages since I've done it, so I've kinda forgotten.
A little help would be great.

InteGrand · May 20, 2015

MysteryMoon said:
Find the equation of the locus of a point that moves so that it is equidistant from point (2,-3) and line y=7
The answer is x^2 - 4x + 20y -36 = 0

I remember being able to do this before but it's been ages since I've done it, so I've kinda forgotten.
A little help would be great.

$Let the point be $P(x,y)$. We want to find the locus of $P$. The squared distance of $P$ to the point $(2,-3)$ is $(x-2)^2 + (y+3)^2$. The squared distance of $P$ to the line $y=7$ is $(y-7)^2$. For these distances to be equal, we have:$

$(x-2)^2 + (y+3)^2=(y-7)^2\Rightarrow x^2 -4x + 4 + y^2 + 6y + 9 = y^2 -14y + 49$

$$\Rightarrow x^2 -4x +20 y -36 = 0$ (this is the locus).$

Can anyone help me with this locus question? (1 Viewer)

MysteryMoon

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InteGrand

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