Jenny asked in Science & MathematicsMathematics · 7 months ago

# 54. Identify the center of the parabola (y + 5)2 = 8x − 4.?

54) Identify the center of the parabola (y + 5)2 = 8x − 4.

okay so is it asking for vertex? is center same as vertex in which i got (1/2 , -5) ?

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• 7 months ago

(y + 5)^2 = 8x − 4

(y + 5)^2 + 4 = 8x

x = 1/8(y + 5)^2 + 1/2

yeh, it's (1/2, - 5)

This will be the graph look like.

• 7 months ago

Note that parabola has no center! you got a

right answer but it was the vertex, not the center.

• Pope
Lv 7
7 months ago

No, of course the vertex is not the center. A parabola has no center, but the curve is a limiting case of a hyperbola or ellipse. It sometimes is useful to employ a special definition allowing the center to be a point at infinity. In this case it would be the point at infinity on the line y + 5 = 0.

It would be better though simply to answer that the parabola has no center. Do not change the question to suit the answer. You were not asked for the vertex.

• 7 months ago

(y + 5)^2 = 8 x - 4

parabola

focus | (5/2, -5) = (2.5, -5)

vertex | (1/2, -5) = (0.5, -5)     <----

semi-axis length | 2

focal parameter | 4

eccentricity | 1

directrix | x = -3/2

Lv 7
7 months ago

(y+5)² = 8x-4

8x = (y+5)² + 4

x = ⅛(y+5)² + ½

This is a horizontal parabola with vertex (½,-5).

Axis of symmetry: y = -5