Find the standard equation of the parabola which satisfies the given condition below

Question

axis of symmetry y = 9, directrix x = 24, vertex on the line 3y −5x = 7

I've already researched for any similar problem like this but so far I found none.  "vertex on the line 3y-5x=7" confuses me but I'm fine with the rest.

Answer 1

The axis of symmetry in this case is the y coordinate of the vertex. The vertex also lies on the line $3y-5x=7$

Therefore $$3(9)-5x=7$$ and on... $$27-5x=7$$

$$-5x=-20$$

$$x=4$$

So the vertex is $(4,9)$

You said you're fine with everything else so the question can be simplified to: Find the equation of the parabola with directrix $x=24$ and vertex $(4,9)$