Question

A point P(x,y) is such that its distance form the y-axis is equal to its distance

from the point A(3,2).show that y^2 - 4y - 6x + 13 = 0​

Answer 1

Good evening,

Step-by-step

let D represent distance of P form the y-axis

D²=|x|² = x²

AP²=(x-3)²+(y-2)²

D² = AP² ⇌ x² = (x-3)²+(y-2)² ⇌ x² = (x²-6x+9)+(y²-4y+4)

⇌ 0 = -6x+9+y²-4y+4

⇌ y² - 4y - 6x + 13 = 0​.

:)