A parabola is drawn with focus at (3,4) and vertex at the focus of the parabola ${\mathrm{y}}^2-12\mathrm{x}-4\mathrm{y}+4=0$. The equation of the parabola is

${\mathrm{y}}^2-12\mathrm{x}-4\mathrm{y}+4=0\Rightarrow (\mathrm{y}-2{)}^2=12\mathrm{x}$

Its vertex is (0,2) and a = 3,
Its focus = (3, 2).
Hence, for the required parabola; focus is (3,4) vertex =(3,2) and a = 2,
Hence, the equation of the parabola is $(\mathrm{x}-3{)}^2=4(2\left)\right(\mathrm{y}-2)$
or   ${\mathrm{x}}^2-6\mathrm{x}-8\mathrm{y}+25=0$