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Tangent Equation

  1. Aug 1, 2005 #1
    Hi any idea on this please.

    Find the values of constant A,B and C if the ellipse 4x^2 +y^2+Ax+By+C=0 is to be tangent to the x axis at the origin and to pass through the point P(-1,2)
     
  2. jcsd
  3. Aug 1, 2005 #2
    what i would do first is to put the equation into a form more readable as far as ellipces aree concerned
     
  4. Aug 2, 2005 #3
    You can also do it straight ahaid:

    (1) The ellipse must pass through (0,0). What does this tell you about C?

    (2) The ellipse must be tangent to the x-axis too. So the normal to the ellipse can not have an x-component. Recall that the gradient of a function is perpendicular to it's constant value curves. So the normal to the ellipse at the origin is given by the gradient of [tex]4x^2 +y^2+A x+B y+C[/tex] at (0,0). This gives us A.

    (3) Just plug in the point P to find the remaining unknown B.
     
  5. Aug 2, 2005 #4
    Dini's theorem: [tex]g(x_0, y_0)=0 [/tex] and [tex] \nabla g|_{(x_0, y_0)} \neq \vec 0[/tex], then

    [tex]\exists h(x) : g(x, h(x)) = 0 [/tex] and

    [tex]h'(x)=\frac {g_x} {g_y}[/tex]
     
  6. Aug 5, 2005 #5
    I didn`t got u on getting constant Value C Timbuqtu
     
  7. Aug 6, 2005 #6

    TD

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    Homework Helper

    Fill in the point (0,0) and you'll find immediately that c = 0.
    If not, the ellipse wouldn't go through the origin.
     
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