The equation of the parabola whose focus is at (7, 0) and directrix at x = -7 is:
Accepted Solution
A:
The directrix x=-7 must be perpendicular to the axis that goes through the focus (7,0), then the axis of this parabola is y=0 The directrix cuts the axis of the parabola at the point (-7,0)
The vertex of the parabola V=(h,k) is the midpoint of the points (-7,0) and (7,0= h=(-7+7)/2=(0)/2→h=0 k=(0+0)/2=(0)/2→k=0 Vertex: V=(h,k)→V=(0,0)
As the axis of the parabola is horizontal, the parabola has an equation of the form: (y-k)^2=4p(x-h)
The parabola opens to the right then p is positive (p>0) p is the distance between the vertex and the focus, the p=7
(y-k)^2=4p(x-h) (y-0)^2=4(7)(x-0) y^2=28x
Answer: The equation of the parabola whose focus is at (7, 0) and directrix at x = -7 is: y^2=28x