Need help with H2 maths qn.

• meyoi

  14 Jan 12, 22:57

  Pls help with this qn.

  
  A hyperbola with equation y^2+Ay+Bx^2+Cx+D=0, where A,B,C and D are real constants, passes through the pt (5/3, 17) and has a maximum pt at (-1,1). Find A,B and C.

   

   

   

• wee_ws

  15 Jan 12, 09:26

  Hi,

    1. Form equation 1, since (5/3, 17) lies on the curve.

    2. Form equation 2, since (-1, 1) lies on the curve.

    3. Differentiate the equation implicitly. Form equation 3, since dy/dx = 0 when x = -1.

    4. Use GC App to solve for A, B, C in terms of D.

    Thanks.

  Cheers,
  Wen Shih

• meyoi

  15 Jan 12, 15:13

  Hi, thanks for the reply.

  I have tried using the above mentioned pts to form the 3 equations, but they are not enough to solve the unknown values( the answers given are A=-14, B=-9 and C=-18). How do i form the 4th equation?

   

   

• wee_ws

  15 Jan 12, 15:43

  Hi,

    Using your answers, I found D = 4 with the point (-1, 1).

    However, with these four values, the point (5/3, 17) does not satisfy the equation.

    You may wish to check with your school if something is amiss about this question.

    Thanks.

  Cheers,
  Wen Shih

• SBS2601D

  15 Jan 12, 15:53

  Question is flawed through and through.

  The equation is either that of a ellipsoid, or a quadratic curve with a single stationary point.

  There can be no y value higher than 1.

  No need to even start working out.

• meyoi

  15 Jan 12, 18:10

  Hi Wen Shih,

  the given pt (5/3,17) does satisfy the given eqn.

  Chk: y^2+Ay+Bx^2+Cx+D=0

  (17)^2 - 14(17) - 9(5/3)^2 - 18(5/3) + 4 = 0.

   

   

• wee_ws

  15 Jan 12, 18:34

  Hi meyoi,

    Yes, I realised I made a careless mistake in the substitution process :P

    Still, I think one piece of information is missing for us to form the fourth equation.

  Cheers,
  Wen Shih

• wee_ws

  15 Jan 12, 18:43

  Hi,

    From the information, one can gather that

    - the curve is symmetrical about x = -1, since we are given the max point,

    - the curve is symmetrical about y = -A/2, by completing the square on y^2 + Ay,

    - by point 3 (I mentioned above) B and C are related by C = 2B.

    The resulting curve based on the answer given has the above properties.

    Thanks.

  Cheers,
  Wen Shih

• SBS2601D

  15 Jan 12, 20:18

   

  Gaussian elimination?

   

• wee_ws

  16 Jan 12, 07:25

  Hi,

    Gaussian elimination is not covered in H2 Maths.

    We may reword the 'problematic' question like this, since Cambridge examiners typically provide obvious information and kindly guidance:

    A hyperbola H has equation y^2+Ay+Bx^2+Cx+D=0, where A, B, C and D are real constants. H is symmetrical about the line y = 7, has a maximum point at (-1, 1) and passes through the point (5/3, 17).

  (i) State the value of A.

  (ii) Write down the coordinates of the minimum point on H.

  (iii) Find the values of B, C and D.

    Thanks.

  Cheers,
  Wen Shih