Question 1071454
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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^2/4^2 + y^2/3^2}}} = 1.


The linear eccentricity of this ellipse is c = {{{sqrt(4^2 - 3^2)}}} = {{{sqrt(16-9)}}} = {{{sqrt(7)}}}.


You may find useful the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Ellipse-definition--canonical-equation--characteristic-points-and-elements.lesson>Ellipse definition, canonical equation, characteristic points and elements</A>

in this file.
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All questions are answered.



On ellipses, you have the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Ellipse-definition--canonical-equation--characteristic-points-and-elements.lesson>Ellipse definition, canonical equation, characteristic points and elements</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Ellipse-focal-property.lesson>Ellipse focal property</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Tangen-lines-to-a-circle.lesson>Tangent lines and normal vectors to a circle</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Tangent-lines-to-an-ellipse.lesson>Tangent lines and normal vectors to an ellipse</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Optical-property-of-an-ellipse.lesson>Optical property of an ellipse</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Optical-property-of-an-ellipse-revisited.lesson>Optical property of an ellipse revisited</A>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Identify-vertices-co-vertices-foci-of-the-ellipse-given-by-an-equation.lesson>Identify the vertices, co-vertices and foci of the ellipse given by an equation</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Find-a-standard-equation-of-an-ellipse-given-by-its-elements.lesson>Find a standard equation of an ellipse given by its elements</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Find-the-equation-of-the-circle-given-by-its-center-and-tauching-a-given-line.lesson>Find an equation of the circle given by its center and tauching a given line</A>

in this site.