write the equation for a parabola with a focus at (-7, -5) and a directrix at y=-4

Question

write the equation for a parabola with a focus at (-7, -5) and a directrix at y=-4

Answer 1

The axis of symmetry of the parabola is perpendicular to the directrix and passes through the focus.

So, axis of symmetry is the vertical line x = -7.

The vertex of the parabola lies on the axis of symmetry and is halfway between the focus and directrix.

So, vertex = (-7, -4.5)

p = directed distance between vertex and focus. Since the focus lies below the vertex, p = -1/2.

Equation of parabola: y - (-4.5) = (1/(4p)) (x - (-7)²

y + 4.5 = -(1/2)(x + 7)²