x22x8y9 0 2x2 2x y 5 0 Solutionx2 2x 8y 9 0 x2 2x 1 8y

x^2-2x+8y+9 = 0 2x^2 - 2x - y - 5 = 0

x^2 - 2x +8y +9 =0

(x^2 -2x +1) +8y +8 =0

(x-1)^2 +8 = -8y

y = -(1/8)(x-1)^2 -1

Its inverted downwards parabola

Standard equation : y = 4p(x-h)^2 +k

Vertex : ( 1 , - 1)

4p = 1/8 ---> p = 1/32

Focus : (1 , -1 -1/32) = (1 , - 1.03125)

Axis of symmetry: x = 1 ( Vertical)

Directrix: y = k - p = -1 - 1/32 = - 1.03125

y = -1.03125

Parabola opens down