Find the vertex, focus, and directrix for the parabolas: a) (y–9)2=8(x−2) b) y2–4y=4x–22 c) (x–6)2=4(y–2)

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ossidianaZ

2021-01-04

Find the vertex, focus, and directrix for the parabolas:
a)

{(y - 9)}^{2} = 8 (x - 2)

y^{2} - 4 y = 4 x - 2^{2}

{(x - 6)}^{2} = 4 (y - 2)

funblogC

Skilled2021-01-05Added 91 answers

{(y - 9)}^{2} = 8 (x - 2)

{(y - k)}^{2} = 4 p (x - h)

h = 2, k = 9,

4 p = 8

p = \frac{8}{4} = 2

vertex

= (h, k) = (2, 9)

focus

= (4, 9)

directrix

= x = h - p = 2 - 2 = 0

y^{2} - 4 y = 4 x - 2^{2}

– transform, as

a^{2} + b^{2} + 2 a b = {(a + b)}^{2}

, so

y^{2} - 4 y + 4 = 4 x + 4 + 4

{(y - 2)}^{2} = 4 (x + 2)

h = - 2, k = 2

4 a = 4

a = 1

vertex

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

focus

= (- 2, 3)

directx

= h - p = - 2 - 3 = - 5

{(x - 6)}^{2} = 4 (y - 2)

{(x - h)}^{2} = 4 p (y - k)

h = 6, k = 2

4 p = 4

p = 1

vertex

= (h, k) = (6, 2)

focus

= (h, k + p) = (6, 3)

directrix

= k - p = 2 - 1 = 1

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