Tangent Equation

  • Thread starter kidia
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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)
 

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208
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what i would do first is to put the equation into a form more readable as far as ellipces aree concerned
 
83
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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.
 
92
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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]
 
66
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I didn`t got u on getting constant Value C Timbuqtu
 
TD
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kidia said:
I didn`t got u on getting constant Value C Timbuqtu
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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