Question

find focus, diretrix, axis, vertex of parabola y^2-4x-6y+25=0​

Answer 1

Answer:

y2+8x+6y+25=0⟹(y2+6y+9)−9+8x+25=0

(y+k)2=4p(x−h)⟹(y+3)2=−8x−16⟹(y+3)2=−8(x+2)

(y+3)2=4(−2)(x+2)

The axis of symmetry is y = -3, the vertex is at (-2, -3), the focus is at (-2 + -2, -3) = (-4,-3) and the directrix is x = -2 -(-2) = 0

Answer 2

Answer:

y2+8x+6y+25=0⟹(y2+6y+9)−9+8x+25=0

(y+k)2=4p(x−h)⟹(y+3)2=−8x−16⟹(y+3)2=−8(x+2)

(y+3)2=4(−2)(x+2)

The axis of symmetry is y = -3, the vertex is at (-2, -3), the focus is at (-2 + -2, -3) = (-4,-3) and the directrix is x = -2 -(-2) = 0

Step-by-step explanation:

The equation of the directrix for the parabola y² + 8x + 6y +25 = 0 is x = 0.