Aspire Faculty ID #3641 · Topic: NIMCET 2012 · Just now
NIMCET 2012

The equation of ellipse with major axis along the x–axis and passes through the point $(4,3)$ and $(-1,4)$.

Solution

Ellipse form: 
$\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1,\quad a^2 > b^2$ 

Using points: $\displaystyle \frac{16}{a^2} + \frac{9}{b^2} = 1$ 
$\displaystyle \frac{1}{a^2} + \frac{16}{b^2} = 1$ 

Solve gives: 
$\displaystyle 7x^2 + 15y^2 = 247$ 
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