Find Vertex when Focus and Directrix of Parabola is given.

Question

Focus is $(1,1)$ and equation to the Directrix is $3x+4y-2=0$ I've successfully derived the equation of Parabola in second degree general form which is: $16x^2 - 38x+9y^2 - 34y+46-24xy=0$ Also, find the equation of its axis.

Answer 1

Hint: The axis is the line that is perpendicular to the directrix and passes through the focus. The vertex will be the midpoint of the line segment joining the focus and the intersection of the aforementioned lines.