Question

A parabola can be drawn given a focus of (-4,10) and a directrix of y=-4 write the equation of the parabola in any form

Answer 1

Answer:

$(x+4)^2=28(y-3)$

Step-by-step explanation:

The directrix of the parabola is the horizontal line with the eqaution $y=-4.$ The focus of the parabola is at point (-4,10), than the axis of symmetry of the parabola is the perpendicular line to the directrix passing through the focus. Its equation is $x=-4$

The distance between the directrix and the focus is $|10-(-4)|=14,$ so $p=14$ and the vertex is at point $\left(-4,10-\dfrac{14}{2}\right)\rightarrow (-4,3)$

Parabola goes in positive y-direction, hence its equation  is

$(x-x_0)^2=2p(y-y_0),$

where $(x_0,y_0)$ is the vertex, so the equation of this parabola is

$(x+4)^2=28(y-3)$