geometry

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hich is the equation of a circle with diameter AB with A(5,4) and B(-1,-4)?
possible answers;
(x-5)^2+(y-4)^2=10
(x+5)^2+(y+4)^2=100
(x-2)^2+y^2=25
(x+2)^2+y^2=5
Not sure

  • geometry -

    Standard equation of a circle with a radius of r and centre (x0,y0) is:
    (x-x0)²+(y-y0)²=r²

    Centre of circle:
    ((5-1)/2, (4+(-4))/2)=(2,0)
    Out of the four choices, there is only one that has a centre positioned at (2,0).
    (hint: refer to the standard equation of the circle)

    Radius, r:
    Radius of circle = distance from centre to circumference
    r = sqrt((5-2)^2+(4-0)^2)=5

    This confirms the choice above.
    (hint: refer to the standard equation of the circle)

  • geometry -

    This is what I have but not sure if right
    (x-(-2)^2+(y-3)^2=5^2
    (x+2)^2+(y-3)^2=25

  • geometry -

    I do not have the same answer as you.

    If AB is the diameter, the centre is located at the mid-point between A and B.

    The mid-point between A and B is
    ((Xa+Xb)/2, (Ya+Yb)/2)=(2,0)

    I do not know how you got -2 and 3 for the centre of the circle. Can you explain?

  • geometry -

    I was looking at wrong problem for this one a I got (x+5)^2+(y+4)^2=100

  • geometry -

    Your answer is not correct.
    Please explain how you got
    (x+5)^2+(y+4)^2=100 as your answer.
    Hint:
    Centre of circle is at:
    ((5-1)/2, (4+(-4))/2)=(2,0)

  • geometry -

    (x+2)^2+y^2=5

  • geometry -

    1. Centre is at (2,0)
    but
    (x+2)^2+y^2=5
    has a centre at (-2,0)

    2. radius is 5, so the right hand side should be 5^2=25.

  • geometry -

    Now I'm definitely lost would you mind explaining the whole process so I might understand?

  • geometry -

    I guess you have not read this on Sunday:

    Standard equation of a circle with a radius of r and centre (x0,y0) is:
    (x-x0)²+(y-y0)²=r²

    Centre of circle:
    ((5-1)/2, (4+(-4))/2)=(2,0)
    Out of the four choices, there is only one that has a centre positioned at (2,0).
    (hint: refer to the standard equation of the circle)

    Radius, r:
    Radius of circle = distance from centre to circumference
    r = sqrt((5-2)^2+(4-0)^2)=5

    This confirms the choice above.
    (hint: refer to the standard equation of the circle)

  • geometry -

    Okay, 9+16=25
    so would my answer be (x-2)^2+(y^2)=25
    I thiught you had to take the square rt of 25

  • geometry -

    Yep, you got it, congrats!
    I hope you understand how it works.
    If not, feel free to post.

  • geometry -

    The answer is (x-2)2+y2=25 i just took it on my quiz and all the other answers are wrong!!! so i got it wrong at first!! but this is the correct one!

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