Results 1 to 6 of 6

Math Help - Equation of a circle

  1. #1
    Senior Member euclid2's Avatar
    Joined
    May 2008
    From
    Ottawa, Canada
    Posts
    400
    Awards
    1

    Equation of a circle

    An airport is located at D(0,0) A plane is positioned at C(-9,-16). The radar at the airport covers the area xsquared+ysquared=324. Will the plane show up on the radar at its current position. Explain. I know it wont i just dont know how to mathematically justify that.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by euclid2 View Post
    An airport is located at D(0,0) A plane is positioned at C(-9,-16). The radar at the airport covers the area xsquared+ysquared=324. Will the plane show up on the radar at its current position. Explain. I know it wont i just dont know how to mathematically justify that.
    Translated mathematically, "Will the point C be inside the circle x^2 + y^2 = 324?"

    Translated (co-ordinate)geometrically "Is x=-9, y=-16 such that x^2 + y^2 \leq 324?"

    Now can you solve it?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Smile

    Quote Originally Posted by euclid2 View Post
    An airport is located at D(0,0) A plane is positioned at C(-9,-16). The radar at the airport covers the area xsquared+ysquared=324. Will the plane show up on the radar at its current position. Explain. I know it wont i just dont know how to mathematically justify that.
    Is (-9,\,-16) a solution to the inequality x^2 + y^2\le324? If so, the plane will show up on the radar. Otherwise it will not.

    Here is another method: the radar covers an area of radius \sqrt{324} = 18. So find the distance between the origin and the point (-9,\,-16) and see if it is less than, equal to, or greater than 18.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member euclid2's Avatar
    Joined
    May 2008
    From
    Ottawa, Canada
    Posts
    400
    Awards
    1
    If i plug the numbers in it becomes 337=324, therefore since it is greater on the left side it will not the seen in the radar. Is this all the work necessary to show?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Smile

    Quote Originally Posted by euclid2 View Post
    If i plug the numbers in it becomes 337=324, therefore since it is greater on the left side it will not the seen in the radar. Is this all the work necessary to show?
    Yes.

    (-9)^2 + (-16)^2\le324\Rightarrow337\le324 which is false, so the point does not satisfy the inequality.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by euclid2 View Post
    If i plug the numbers in it becomes 337=324, therefore since it is greater on the left side it will not the seen in the radar. Is this all the work necessary to show?
    Yes its enough and I think thats what is expected. However note that Reckoner's alternate solution is very elegant and mathematically justified
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Circle equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 29th 2010, 06:29 AM
  2. equation of a circle
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 19th 2008, 08:01 AM
  3. equation of circle
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: May 4th 2008, 02:05 PM
  4. Equation of circle
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: March 17th 2008, 04:45 PM
  5. equation of a circle
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 17th 2007, 08:25 PM

Search Tags


/mathhelpforum @mathhelpforum