SOLUTION: an ellipse has an equation of ax^2 +by^2 +f = 0 passing through (4,0) and (0,3) a. find the equation of the ellipse b. find the eccentricity of the ellipse

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: an ellipse has an equation of ax^2 +by^2 +f = 0 passing through (4,0) and (0,3) a. find the equation of the ellipse b. find the eccentricity of the ellipse      Log On


   

Question 1071454: an ellipse has an equation of ax^2 +by^2 +f = 0 passing through (4,0) and (0,3)
a. find the equation of the ellipse
b. find the eccentricity of the ellipse
Answer by ikleyn(52803) About Me  (Show Source):
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This ellipse has the center at (0,0) and has intercepts x = 4 and y = 3.


Hence, its semi-axes are 4 units along the x-axis and 3 units along the y-axis.


It implies that the equation of the ellipse is


x%5E2%2F4%5E2+%2B+y%5E2%2F3%5E2 = 1.


The linear eccentricity of this ellipse is c = sqrt%284%5E2+-+3%5E2%29 = sqrt%2816-9%29 = sqrt%287%29.


You may find useful the lesson

    - Ellipse definition, canonical equation, characteristic points and elements

in this file.

All questions are answered.


On ellipses, you have the lessons
    - Ellipse definition, canonical equation, characteristic points and elements
    - Ellipse focal property
    - Tangent lines and normal vectors to a circle
    - Tangent lines and normal vectors to an ellipse
    - Optical property of an ellipse
    - Optical property of an ellipse revisited

    - Identify the vertices, co-vertices and foci of the ellipse given by an equation
    - Find a standard equation of an ellipse given by its elements
    - Find an equation of the circle given by its center and tauching a given line
in this site.