Expert: Sherman D. - 5/28/2009

Question
1.  What is the vertex of the parabola y = (x + 8)^2 - 2?

2.  Find the center and the radius of the equation x^2 + y^2 = 64

3.  Write the equation in standard form x^2 + y^2 - 4x -14y + 29 = 0.

4.  Write an equation with center (0, 9) and radius sqrt5

5.   Name the axis to which the major axis is parallel and find the center of 9(x + 1)^2 + 27(y - 1)^2 = 81.

Thank you :)

Answer
1.)
vertex formula is y = a(x - h)^2 + k, where (h,k) is the vertex

ANS : (-8,-2)

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2.)
Circle formula is (x - h)^2 + (y - k)^2 = r^2
ANS : Center is (0,0) and Radius is 8

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3.)
x^2 + y^2 - 4x - 14y + 29 = 0
x^2 - 4x + y^2 - 14y = -29
(x^2 - 4x + 4 - 4) + (y^2 - 14y + 49 - 49) = -29
(x - 2)^2 + (y - 7)^2 = 24

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4.)
x^2 + (y - 9)^2 = 5

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5.)
9(x + 1)^2 + 27(y - 1)^2 = 81
((x + 1)^2 / 27) + ((y - 1)^2 / 9) = 1

Equation of an ellipse is ((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1

Center is (-1,1)
The Axis that is parallel to the major axis is the X-axis

just google circle formula, vertex formula, and ellipse