Find the standard equation of the parabola with vertex (0,0) and focus (0,3). In which direction does the parabola open?

Determine the location of the focus and the directrix of the parabola y + 6y – 8x- 23 = 0. O Focus: (-4, -1) Directrix: y = -5 O Focus: (-4, -5) Directrix: y = -1 O Focus: (-6, -3) Directrix: x = -2 Focus: (-4, -3) Directrix: y = -3 O Focus: (-2, -3) Directrix: x = -6

Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse axis 6 and the curve passes through the point (7, -4).