Answer to Question #281668 in Analytic Geometry for Jackie

Question

Write an equation for the set of all points in the plane equidistant from (0,–6) and y= –10.

Write your answer in vertex form. Simplify any fractions.

Answer 1

Let the parametric point be (x,y) on the plane which is equidistant from the given point (0,6)  hence, we have

$\sqrt{x^2+(y+6)^2}=y+10\\ =x^2+y^2+12y+36=(y+10)^2\\ = x^2+y^2+12y+36=y^2+20y+100\\ =x^2-8y-64=0$