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Easy question
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1) 4x^2 + 8x +4y^2 +16y -13 = 0
Find the center and radius of the circle

2) Given three points on a parabola as (0,4) (4,4) (8,12), determine the equation for that parabola.
put in y=ax^2+bx+c to from a system of three linear equations

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amna04352

Answer:

1) Centre: (-4,-8)

Radius: sqrt(93)

2) y = ¼x² - x + 4

Step-by-step explanation:

1) 4x² + 8x +4y² +16y -13 = 0

h = -8/2 = -4

k = -16/2 = -8

(-4)² + (-8)² - (-13) = r²

r² = 93

r = sqrt(93)

sqrt: square root

2) h = (0+4)/2 = 2

y = a(x - 2)² + k

4 = a(0-2)² + k

4 = 4a + k

k = 4 - 4a

12 = a(8-2)² + k

12 = 36a + k

12 = 36a + 4 - 4a

8 = 32a

a = ¼

k = 4 - 4(¼) = 4 - 1 = 3

y = ¼(x - 2)² + 3

y = ¼(x² - 4x + 4) + 3

y = ¼x² - x + 1 + 3

y = ¼x² - x + 4