<p>Which equation describes the set of all points (x,y) that are equidistant from the x-axis and the pt (4,6)?</p>
<p>Can someone provide the answer as well as the explanation for me?
Much appreciated.</p>
<p>its a conic section of a parabola… i dont know the exact answer but im studying conics later this week. it should be something like for some constant a: a(x-4)^2+3</p>
<p>distance of point [x,y] on the line from 4,6 is same as that from line y=0;
hence,
((x-4)^2 + (y-6)^2)^1/2 = distance from y=0; Its difficult to type all of that here,
simplify that you will get
y^2=4ax form,
so its a parabola,</p>
<p>In very simple manner,
Its just from the definition. A parabola is the locus of a point which is equidistant from the directrix[here, x-axis], and a focus [here, (4,6)].
Its that simple.</p>