- #1

kidia

- 66

- 0

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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- Thread starter kidia
- Start date

- #1

kidia

- 66

- 0

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

mathmike

- 208

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- #3

Timbuqtu

- 83

- 0

(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.

- #4

Maxos

- 92

- 0

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

[tex]h'(x)=\frac {g_x} {g_y}[/tex]

- #5

kidia

- 66

- 0

I didn`t got u on getting constant Value C Timbuqtu

- #6

TD

Homework Helper

- 1,022

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Fill in the point (0,0) and you'll find immediately that c = 0.kidia said:I didn`t got u on getting constant Value C Timbuqtu

If not, the ellipse wouldn't go through the origin.

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