find length of semi major axes of ellipse

Question

suppose that equation of ellipse is given by

$4x^2+3*y^2=25$ we should length of major axes ,first let us transform this equation into standard form or divide by $25$

$4*x^2/25+3*y^2/25=1$

if we compare it to $x^2/a^2+y^2/b^2=1$;we get that $a=5/2$ and $b=5/\sqrt{3}$;so it means that as i know major axes$=2*a$,therefore major axes=5 right?but in book it is equal to $10/\sqrt{3}$,why it is so?please help me

Answer 1

The length of a semi major axis is just $b$, if the equation of the ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ where $a<b$ which here is $\frac5{\sqrt3}$

Answer 2

Because the major axis is that which is the longer of the two axes. Since $\sqrt{3} < 2$, your $b$ is actually the major axis.