find the equation of the locus of a moving point which is always equidistant from the y-axis and the point (-6,4)

Question

Do you know how to solve its equation? Already solved some locus problems that gives points but not in the y or x axis problems.

Answer 1

If the point is $(a,b)$, its distance from the $y$ axis is $a$ and its distance from $(-6,4)$ is ??? Equate these and you have your equation. It should be a parabola-this is one definition of a parabola.

Answer 2

Let $(x, y)$ be the unknown point. It's distance from the $y$ axis is given by $|x|$. It's distance from the point $(-6, 4)$ is given by $$d = \sqrt{(x - (-6))^2 + (y - 4)^2}$$

Now put $|x| = d $, and you're done, though you could, of course, simplify the equation:

$$x^2 = (x + 6)^2 + (y - 4)^2$$ and then simplify a bit more.