Question

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

Answer 1

Since the major axis is along x - axis. So the equation of ellipse in standard form is,
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Since the ellipse passes through point (4,3)
$\therefore \frac{16}{a^2}+\frac{9}{b^2}=1$
Also the ellipse passes through point (6, 2)
$\therefore \frac{36}{a^2}+\frac{4}{b^2}=1$
Solving (i) and (ii), we have,
$a^2=52and{b}^2=13$
Thus equation of required ellipse is,
$\frac{x^2}{52}+\frac{y^2}{13}=1.$