Results 1 to 3 of 3

Math Help - Circles?

  1. #1
    Senior Member
    Joined
    Dec 2010
    From
    CPT
    Posts
    302

    Circles?

    Write the equation of the circle that satisfies each set of conditions.

    1.The endpoints of the diameters are (5,6) and (2,3)?

    2. The circle passes through origin and has its center at (-4,3).

    Now I know the standard form of the equation of a circle is

    (x-h)^2+(y-k)^2=r^2

    But how would I solve these two problems I mean for number 2 I know x and y but no the radius.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,857
    Thanks
    321
    Awards
    1
    Quote Originally Posted by homeylova223 View Post
    Write the equation of the circle that satisfies each set of conditions.

    1.The endpoints of the diameters are (5,6) and (2,3)?

    2. The circle passes through origin and has its center at (-4,3).

    Now I know the standard form of the equation of a circle is

    (x-h)^2+(y-k)^2=r^2

    But how would I solve these two problems I mean for number 2 I know x and y but no the radius.
    1) You have two points on the circle and you know they represent a diameter. How do you find the diameter from this? The center of the circle is at the center of the diameter. How do you find this?

    2) You have the center so what is h and k? You also have a point on the circle. What then, in addition to knowing the center, can you do with that? (Hint: Plug (0, 0) into the circle equation, or note that the line between (0, 0) and (-4, 3) is a radius.)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by homeylova223 View Post
    Write the equation of the circle that satisfies each set of conditions.

    1.The endpoints of the diameters are (5,6) and (2,3)?

    2. The circle passes through origin and has its center at (-4,3).

    Now I know the standard form of the equation of a circle is

    (x-h)^2+(y-k)^2=r^2

    But how would I solve these two problems I mean for number 2 I know x and y but no the radius.
    For the first note use the distance formula to find the length of the diamater.

    d=\sqrt{(6-3)^2+(5-2)^2}=\sqrt{3^2+3^2}=3\sqrt{2}

    So the radius is half of the diameter we get that

    r=\frac{1}{2}(3\sqrt{2})=\frac{3\sqrt{2}}{2} \implies r^2=\frac{9}{2}

    and the center is at the midpoint so we get

    x=\frac{5+2}{2}=\frac{7}{2} \quad y=\frac{6+3}{2}=\frac{9}{2}

    For the 2nd one use the distance formula to find the radius then just plug into the formula
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove that every rigid motion transforms circles into circles
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: February 11th 2010, 06:00 PM
  2. Replies: 2
    Last Post: October 6th 2009, 08:04 AM
  3. 4 circles
    Posted in the Geometry Forum
    Replies: 3
    Last Post: July 26th 2009, 10:15 AM
  4. going in circles
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: July 23rd 2009, 10:57 AM
  5. Circles - Please Help
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: October 9th 2008, 07:36 PM

Search Tags


/mathhelpforum @mathhelpforum