Find the equation of an ellipse whose axes lie along coordinate axes and which passes through (4,3) and (-1,4).
Equation of ellipse is x2/a2 + y2/b2 = 1 …. (1)
It is given that (4,3) and (1,4) pass through an ellipse
By putting (4,3) in the equation 1,
We get, (4)2/a2 + (3)2/b2 = 1
Or 16/a2 +9/b2 =1
By putting (-1,4) in the equation 1,
We get, (-1)2/a2 + (4)2/b2 = 1
Or 1/a2 +16/b2 =1
Hence, it is found that b2 = 247/15 (By solving for b2)En cHdenwe cHenecv
Therefore a2 = 247/7
Therefore, ellipse equation is 7x2 + 15y2 = 247
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