posted by Moana .
how to find the equation of a parabola given foci(-7,-17), (-7,17
),the absolute value of the difference of the distances of any point from the foci is 24
A parabola has only one focus. You mean a hyperbola.
Now, since the distances to the foci differ by 24, and the foci are 34 apart, you have a hyperbola with
a = 12
c = 17
b = √145
Since the center is at (-7,0) and the foci are on the line x = -7, the hyperbola is
y^2/145 - (x+7)^2/144 = 1