A parabola can be drawn given a focus of (7, -3)(7,−3) and a directrix of x=-7x=−7. What can be said about the parabola?

Question

The parabola has a vertex at (, ), has a p-value of  and it  opens upopens downopens leftopens right.

Answer 1

If directrix= -7 and focus = (7,-3) the vertex is the midpoint between (7,-3) and (-7,-3) = (0,-3)

the parabola opens to the right. It's of the form x=a(y+3)^2

to solve for a, plug in another point on the parabola, directly above the focus (7,y) the distance from y to -3 is the same as from 7 to -7 = 14. 14-3 = 11, the point on the parabola is (7,11) plug that in to solve for a

7 = a(11+3)^2= 14^2(a)

a = 7/14^2 = 1/28

the parabola is x = (1/28)(y+3)^2 or

28x = (y+3)^2

the axis of symmetry is y=-3, the line through the focus and vertex and perpendicular to the directrix

the latus rectum is the distance from (7,11) to (7,-17), the two points on the parabola directly above and below the focus.

the parabola opens rightward when the focus is to the right of the directrix

the absolute value of p is the distance from the vertex to the focus or 7

1/4p = a, the coefficient of y^2 = 1/28