Question

Find the the length of the major axis of ellipse: $12x^2+4y^2+24x-16y+25=0$

• A. $\sqrt{3}$
• B. $2\sqrt{3}$
• C. $2\sqrt{\frac{3}{2}}$
• D. $2\sqrt{6}$

Answer 1

The correct option is A $\sqrt{3}$

$12x^2+4y^2+24x-16y+25=0$

$\Rightarrow 12(x^2+2x+1)+4(y^2-4y+4)=3$

$\Rightarrow 12(x+1{)}^2+4(y-2{)}^2=(\sqrt{3}{)}^2$

$\Rightarrow \frac{{(x+1)}^2}{{\left(\frac{1}{2}\right)}^2}+\frac{{(y-2)}^2}{{\left(\frac{\sqrt{3}}{2}\right)}^2}=1$

Length of major axis $=2a=\sqrt{3}.$