Find the equation of the locus of a point which moves so that it's distance from (4,-3) is always one-half its distance from (-1,-1).
[Math] Find the equation of a locus…(Read More)
analytic geometrygeometrylocus
analytic geometrygeometrylocus
Find the equation of the locus of a point which moves so that it's distance from (4,-3) is always one-half its distance from (-1,-1).
Best Answer
The writing is almost automatic: $$\sqrt{(x-4)^2+(y+3)^2}=\frac{1}{2}\sqrt{(x+1)^2+(y+1)^2}.$$ You will find it worthwhile to simplify. Square both sides. After some manipulation, you will find that the locus is a circle, of which you can find the centre and radius.
Remark: If what I called almost automatic is not quite as automatic as I think, please leave a message and I can amplify.