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Math Help - find the vertex, focus, & directrix

  1. #1
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    find the vertex, focus, & directrix

    (y-2)^2=4(x+3)

    i got the vertex--(2,-3)
    but am having trouble finding the focus and directrix.
    i know the x coordinate of the focus is -2, but i'm not sure how to find the y coordinate. my teacher told us to take the number out in front on the right, in this case 4, and divide by 4. so, the answer is 1. but the answer in the back of the book is (-2,2). do i just add one to 4/4? if so, do i always?

    thanks in advance.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by beetz View Post
    (y-2)^2=4(x+3)

    i got the vertex--(2,-3)
    but am having trouble finding the focus and directrix.
    i know the x coordinate of the focus is -2, but i'm not sure how to find the y coordinate. my teacher told us to take the number out in front on the right, in this case 4, and divide by 4. so, the answer is 1. but the answer in the back of the book is (-2,2). do i just add one to 4/4? if so, do i always?

    thanks in advance.
    see post #2 here
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  3. #3
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    i don't get the right answer with the formulas you posted.

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

    the problem: (y-2)^2=4(x+3)

    focus: (h + p, k) = -3+1 =-2 or, if i don't attach a negative sign, 3+1=4.
    k=-2, so (-2,-2) or (4,-2). the answer is (-2,2).

    what am i doing wrong?
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  4. #4
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    wait, so you change the sign of k and h in the problem?

    that would give me the right answer
    h=-3, k=2, p=1
    focus-(h+p,k)=-3+1=-2 and 2--> (-2,2)
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by beetz View Post
    wait, so you change the sign of k and h in the problem?

    that would give me the right answer
    h=-3, k=2, p=1
    focus-(h+p,k)=-3+1=-2 and 2--> (-2,2)
    yes, you have to change the sign
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