Find the equation of an ellipse whose axes lie along coordinates axes and which passes through (4, 3) and (- 1, 4).


Given that we need to find the equation of the ellipse passing through the points (4,3) and (- 1,4).



Let us assume the equation of the ellipse as (a2>b2). - - - - (1)


Substituting the point (4,3) in (1) we get





16b2 + 9a2 = a2 b2 ..... - - (2)


Substituting the point (- 1,4) in (1) we get





b2 + 16a2 = a2b2 ..... - - (3)


(3)×16 - (2)


(16b2 + 256a2) - (9a2 + 16b2) = (16a2b2 - a2b2)


247a2 = 15a2b2


15b2 = 247



From (3)






The equation of the ellipse is




7x2 + 15y2 = 247


The equation of the ellipse is 7x2 + 15y2 = 247.


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