How do you write an equation of an ellipse in standard form given vertices (6, 0), (-6, 0) and co-vertices (0, 2), (0, -2)?

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Answer 1 · 2017-10-26T12:41:43

The equation of the ellipse is $x^2+9y^2=36$

Vertices of the Major axis of ellipse are $(a,0) , (-a,0)$

or $(6,0) , (-6,0)$ and vertices of the Minor axis of ellipse are

$(0,b) , (0,-b)$ or $(0,2) , (0,-2)$

Equation of an ellipse with its major axis on the x-axis and minor

axis on the y-axis is: $x^2/a^2 + y^2/b^2 = 1 ; a and b$ are the length

of semi major axis and semi minor axis. Here major axis is

$2a=6+6=12 :. a=6$ and minor axis is

$2b=2+2=4 :. b=2$ . Hence the equation of the ellipse is

$x^2/6^2 + y^2/2^2 = 1 or x^2/36 + y^2/4 = 1 or x^2+9y^2=36$ [Ans]