Answer:
An parabola has focus at( -43/4, 4) and directrix x = -13/4.
The vertex is exactly between focus and directrix, then:
=> vertex ([(-43/4 + (-13/4)]/2, 4) = (-28/4, 4) = (-7, 4)
The directrix x = -13/4 is a vertical line, this parabola is thus a sideways parabola (that looks left or right, not upward or download). It has the equation form as following:
4p(x – h) = (y – k)^2
with vertex(h, k) and p is distance from vertex to directrix
p = |-7 - (-13/4)| = |-15/4| = 15/4.
However, the vertex (-7, 4) is on the left of directrix x =-13/4, then this parabola faces left. Therefore p should be -15/4, not 15/4
=>4*(-15/4)*(x - (-7)) = (y - 4)^2
=>Solution: -15(x + 7) = (y - 4)^2
Hope this helps!
:)