Explanation:

To determine the equation of the line where the point (x, y) is equidistant from (2a, 0) and (0, 3a), use the property of equidistant points from two specific points.

- Start by calculating the distance from (x, y) to (2a, 0):

$\sqrt{(x-2a{)}^2+(y-0{)}^2}$

- Calculate the distance from (x, y) to (0, 3a):

$\sqrt{(x-0{)}^2+(y-3a{)}^2}$

- Set these distances equal:

$\sqrt{(x-2a{)}^2+y^2}=\sqrt{x^2+(y-3a{)}^2}$

- Square both sides and simplify:

$(x-2a{)}^2+y^2=x^2+(y-3a{)}^2$

- Further simplify:

$x^2-4ax+4a^2+y^2=x^2+y^2-6ay+9a^2$

- Solving this gives:

$4ax-6ay=5a^2$

- Simplify the equation by dividing the whole equation by 'a' (assuming a ? 0):

$4x-6y=5a$

So the final equation is:

$$4x-6y-5a=0$$

- Compare with the given options:

- Option 1: 2x - 3y = 0

- Option 2: 3x - 2y = 0

- Option 3: 4x - 6y + 5a = 0

- Option 4: 4x - 6y - 5a = 0