Question

Find the equation for the ellipse that satisfies the given conditions:Major axis on the x-axis and passes through the points (4,3) and (6,2).

Answer 1

Given that :

The major axis is on the x-axis, and the equation of the ellipse will be of the form $\dfrac{x^2}{b^2} +\dfrac{y^2}{a^2} = 1 ....(1)$, (where ‘$a$’ is the semi-major axis.)
The ellipse passes through points $(4, 3)$ and $(6, 2)$.

Hence,
$\dfrac{16}{a^2} \+ \dfrac{9}{b^2} = 1…. (2)$

$\dfrac{36}{a^2} \+ \dfrac{4}{b^2} = 1 …. (3)$
On solving equations (2) and (3), we obtain $a^2= 5^2$ and $b^2= 13$
Thus, the equation of the ellipse is $\dfrac{x^2}{5^2} +\dfrac{y^2}{13} = 1$