Write the equation of a parabola with a vertex at (-5, 2) and a directrix y = -1

Question

need help please.

Answer 1

 The directrix equation is y = -1 and vertex (-5, 2)

Standard  equation parabola  is (x - h )² = 4p (y - k ),

where (h , k ) = vertex and p = directed distance from vertex to focus.

( h , k ) = (-5 , 2)

Directrix equation is  y = k - p

Substitute the y and p  values.

-1 = 2 - p

-1 - 2 = -p

-p  = -3

p  = 3

p  = 3 then 4p = 12

Substitute the 4p  and (h , k) values in ( x - h )² = 4p ( y - k )

(x + 5)² = 12(y - 2)

Parabola equation is (x + 5)² = 12(y - 2) .