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What is the vertex, directrix, and focus of this porabola?

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(X+2)^2=8y-24

asked Nov 18, 2014 in PRECALCULUS by anonymous

1 Answer

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Given parabola equation : (x+2)² = 8y - 24

8y = ( x - (-2) )² + 24

y = (1/8)( x - (-2) )² + 24/8

y = (1/8)( x - (-2) )² + 3

Compare equation with standard from of parabola [ y = a( x - h )² + k ] and write the coefficients.

a = 1/8 , h = - 2 , k = 3

Vertex : (h , k ) = ( - 2 , 3 )

Directrix = directed distance from vertex to focus p = 1/(4a) = 1/(4(1/8)) = 8/4 = 2

Focus : (h, k + p) = (- 2 , 3+2) = (- 2 , 5 )

Solution : vertex : ( - 2 , 3 ) , Directrix : p = 2  and  Focus : (- 2 , 5 ).

answered Nov 18, 2014 by Shalom Scholar

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