Given focus S(3, 0)

and equation of directrix is:  3x + 4y = 1

=> 3x + 4y - 1 = 0

Let P (x, y) be any point on the required parabola and let PM be the length of the perpendicular from P on the directrix

Then, SP = PM

=> SP² = PM²

=> (x - 3)² + (y - 0)² = {(3x + 4y - 1) /{√(3² + 4² )}²

=> x² + 9 - 6x + y² = (9x² + 16y² + 1 + 24xy - 8y - 6x)/25

=> 25(x² + 9 - 6x + y² ) = 9x² + 16y² + 1 + 24xy - 8y - 6x

=> 25x² + 225 - 150x + 25y² = 9x² + 16y² + 1 + 24xy - 8y - 6x

=> 25x² + 225 - 150x + 25y² - 9x² - 16y² - 1 - 24xy + 8y + 6x = 0

=> 16x² + 9y² - 24xy - 144x + 8y + 224 =

This is the required equation of parabola.