Help how to solve this in geometry find the equation using the directed distance?

help me sir and ma'am how to solved the equation using directed distance
here in question Question: find the equation of the bisector of angles for the pair of line line one 4x+2y=9 line two 2x-y=8 please sir I need your help now and thanks in advanced.

There are two angle bisectors. First write both lines in general form.

4x + 2y - 9 = 0
2x - y - 8 = 0

Any point (x, y) on either angle bisector is equidistant from the two lines, so equate those distances.

|4x + 2y - 9|/√(4² + 2²) = |2x - y - 8|/√(2² + 1²)
(4x + 2y - 9)²/(4² + 2²) = (2x - y - 8)²/(2² + 1²)
5(4x + 2y - 9)² = 20(2x - y - 8)²
(4x + 2y - 9)² = 4(2x - y - 8)²
16x² + 16xy + 4y² - 72x - 36y + 81 = 4(4x² - 4xy + y² - 32x + 16y + 64)
16x² + 16xy + 4y² - 72x - 36y + 81 = 16x² - 16xy + 4y² - 128x + 64y + 256
32xy + 56x - 100y - 175 = 0

That is the locus. It may be factored to find the component lines.

(8x - 25)(4y + 7) = 0

The two bisectors:

8x - 25 = 0
4y + 7 = 0

Find the intersection between those two equations. The slope will be the average, so 3. Then plug in the intersection to y=mx+b to find b.

y=3x+b

These lines are parallel to each other. They do not intersect.