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  1. #1
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    question

    i have 2 questions, the first one i could do, its the second i need help with. 1) determine the coordinates of the centre and the radius of the circle with equation x^2 + y^2 - 6x + 8y = 0. so i put it in its squared form (if thats what you call it. if not, any corrections would be appreciated) like so:
    (x - 3)^2 - 9 + (y + 4)^2 - 16 = 0
    \implies (x - 3)^2 + (y + 4)^2 = 25 so the centre must be (3, -4) and the radius is 5

    the second question which i need help with is:
    find the coordinates of the points P and Q, where the line x = 7 intersects this circle. could someone show me in detail the way you would answer this

    thanks for any help
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  2. #2
    MHF Contributor red_dog's Avatar
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    Replace x in the equation of the circle and solve for y.
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  3. #3
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    ok i tried that, here's what i did:
    made x = 7 in the equation
    (7 - 3)^2 + (y + 4)^2 = 0 \implies 16 + y^2 + 8y + 16 = 0
    \implies y^2 + 8y = -32 \implies y^2 + y = -\frac{32}{8} \implies y^2 + y = -4 \implies y + y = \sqrt {-4} \implies y + y = -2 \implies y = -1 which i think is right so the answer must be (7, -1) but the book gives another answer as well as this which is (7, -7) how would you come to this answer?
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  4. #4
    MHF Contributor red_dog's Avatar
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    No, you're wrong.

    16+(y+4)^2=25\Rightarrow (y+4)^2=9\Rightarrow y+4=\pm 3

    If y+4=3\Rightarrow y=-1

    If y+4=-3\Rightarrow y=-7

    So the points of intersection are (7,-1) and (7,-7)
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