Results 1 to 6 of 6

Math Help - Conics-Hyperbolas, Circle, Parabola Exam Question

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    65

    Conics-Hyperbolas, Circle, Parabola Exam Question

    Greeting I am facing difficulties with certain questions that my teacher said I would need to know for my test which on Wednesday and I was wondering if I can get some help. Any help would be greatly appreciated, if I am correct these are old exam questions, but i am really having a tough time solving these questions. Any help would be greatly appreciated.
    Attached Thumbnails Attached Thumbnails Conics-Hyperbolas, Circle, Parabola Exam Question-0001.jpg   Conics-Hyperbolas, Circle, Parabola Exam Question-0002.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Solid8Snake View Post
    Greeting I am facing difficulties with certain questions that my teacher said I would need to know for my test which on Wednesday and I was wondering if I can get some help. Any help would be greatly appreciated, if I am correct these are old exam questions, but i am really having a tough time solving these questions. Any help would be greatly appreciated.
    to #3:

    1. The origin is the center of the hyperbola. Thus the general equation of the hyperbola is \dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1

    2. You know at least 2 points of the hyperbola: (2,0), (4,2). The coordinates of these points must satisfy the equation of the hyperbola. Plug in the coordinates and solve the system of equations for a and b. I've got a=2~\wedge~b=\sqrt{\dfrac43}

    The equation of the hyperbola is: \dfrac{x^2}{4}-\dfrac{y^2}{\frac43}=1

    3. The points B and D are symmetric by reflection over the x-axis. You only need to know the y-coordinate of B to calculate the distance BD. The x-coordinate of B is 3. Plug in this value and solve the equation of the hyperbola for y:

    \dfrac{9}{4}-\dfrac{y^2}{\frac43}=1~\implies~y^2=\dfrac53

    The point B has the coordinates: \left(3,\ \sqrt{\dfrac53}\right); point D is at \left(3,\ -\sqrt{\dfrac53}\right)

    4. |\overline{BD}|=2 \cdot \sqrt{\dfrac53} \approx 2.582\ cm rounded to the nearest centimeter the distance is 3 cm.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Solid8Snake View Post
    Greeting I am facing difficulties with certain questions that my teacher said I would need to know for my test which on Wednesday and I was wondering if I can get some help. Any help would be greatly appreciated, if I am correct these are old exam questions, but i am really having a tough time solving these questions. Any help would be greatly appreciated.
    to #2:

    1. The radius of the circle is perpendicular to the tangent in point T(9, 4). The slope of the radius is: m_r=\dfrac{4-6}{9-8}=-2. Therefore the slope of the tangent is m_t=\dfrac12

    2. Use the slope-point-formula of a straight line to get the equation of the tangent:

    y=\dfrac12 x - \dfrac12

    3. The corner of the room lies on the tangent at x = 8. Therefore the corner has the coordinates C(8, 3.5)

    the lowest point of the circle has the coordinates L(8, 6-\sqrt{5})

    4. The distance between the corner and the disk is:

    d=|\overline{CL}| = 8-\sqrt{5}-3.5\approx 0.2639. Rounded as requested

    d \approx 0.3
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    May 2009
    Posts
    65
    Thx for the help, however number one is still very confusing it was the hardest out of all of them I find if you can help me with that that would be great. Thx for your help concerning 2 and 3 I understand it perfectly now.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Solid8Snake View Post
    Greeting I am facing difficulties with certain questions that my teacher said I would need to know for my test which on Wednesday and I was wondering if I can get some help. Any help would be greatly appreciated, if I am correct these are old exam questions, but i am really having a tough time solving these questions. Any help would be greatly appreciated.
    to #1:

    I've divided the height of the trophy into 3 different parts: The top distance t in red, the middle distance m in brown and the bottom b distance in blue. (See attachment).

    1. b is the y-value of the hyperbola if x = 10:

    \dfrac{100}4-\dfrac{y^2}{16}=1~\implies~y=-\sqrt{16 \cdot 24}\approx -19.5959

    Therefore \boxed{b = 19.5959}

    2. m is the y-value of the hyperbola if x = 3.5:

    \dfrac{12.25}4-\dfrac{y^2}{16}=1~\implies~y=\sqrt{33}\approx 5.7446

    Therefore \boxed{m = 5.7446}

    3. To calculate t I placed the center of the ellipse on the origin. The semi-axes of the ellipse are A = 4 and B = 8. Thus the equation of this ellipse is:

    \dfrac{x^2}{16}+\dfrac{y^2}{64}=1

    Then t = B + |y(3.5)| (That means that the top distance consists of the semi-axis B (= 8) and the y-value if x = 3.5):

    \dfrac{12.25}{16}+\dfrac{y^2}{64}=1~\implies~y=\pm  \sqrt{15}\approx 3.8730

    Therefore the top distance is: \boxed{t = 8 + 3.8730 = 11.8730}

    4. The total height of the trophy is the sum of the three different distances: \boxed{\bold{H = 27.2135}}
    Attached Thumbnails Attached Thumbnails Conics-Hyperbolas, Circle, Parabola Exam Question-football_pokal.png  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    May 2009
    Posts
    65
    Thx for the help, but it appears your response to number one is wrong the answer i got was 50.13 about and the teacher said the answer should be close to 49 I guess my answer is close enough, thx for the help though it helped me determine how to solve the question.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Conics: Parabola
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 5th 2011, 06:35 PM
  2. Conics-Circle Question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 17th 2009, 10:17 PM
  3. Conics Circle Super simple question
    Posted in the Math Topics Forum
    Replies: 7
    Last Post: May 16th 2009, 08:16 PM
  4. Conics: Quick Circle Question
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: April 22nd 2009, 05:12 AM
  5. Parabola question.... exam ..plz help asap..
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: January 25th 2008, 04:51 PM

Search Tags


/mathhelpforum @mathhelpforum