what is the focus and directrix of (y+1)^2=-8(x-1)

Answer 1

The parabola equation is (y + 1 )² = - 8 (x - 1)

The y  part is squred, so the parabola is horizontal.

Standard form of horizontal parabola is (y - k )² = 4p (x - h )

Rewrite the parabola in standard form [y - (- 1)]² = 4(- 2) (x - 1)

(h, k ) = (1, -1), p  = - 2

p  is negitive, the parabola opens to the left.

Directrix of horizontal parabola x  = h - p

Focus of parabola (h + p , k ).

Directrix x  = 1 - (-2) = 3

Directrix x  = 3.

Focus [ 1 + (-2), - 1] = (- 1, - 1)

Focus = (-1, -1).