Question

PLEASE HELP ASAP! Thanks!!!!! Explain:

Answer 1

Answer:

  (3, 3) and (15, 15)

Step-by-step explanation:

The points equidistant from the given point and the y-axis lie on the parabola that has (3,6) as its focus and the y-axis as its directrix. The equation for that can be simplified from ...

  (x -3)^2 +(y -6)^2 = x^2

  -6x +9 +y^2 -12y +36 = 0 . . . . . subtract x^2, eliminate parentheses

We can find the points that lie on the line y=x (equidistant from both axes) by substituting y for x or vice versa. Then we have the quadratic ...

  x^2 -18x +45 = 0 . . . . substitute x for y and collect terms

  (x -3)(x -15) = 0 . . . . factor it

  x = 3 or 15

So, the points of interest are (x, y) = (3, 3) and (x, y) = (15, 15).