Question

The equation of the axes of the ellipse $4x^2+3y^2-8x+6y-5=0$, are

• A. major axis is $y+1=0$
• B. minor axis is $y+1=0$
• C. minor axis is $x=1$
• D. major axis is $x=1$

Answer 1

Answer: (B), (D)

major axis is $x=1$

$4x^2+3y^2-8x+6y-5=0$
$\Rightarrow 4(x^2-2x+1)+3(y^2+2y+1)=5+3+4$
$\Rightarrow 4(x-1{)}^2+3(y+1{)}^2=12$
$\Rightarrow \frac{(x-1{)}^2}{3}+\frac{(y+1{)}^2}{4}=1$

Hence the axes of the ellipse is parallel to coordinate axes
$\therefore$ centre is at $(1,-1)$
From the equation $b>a$, so ellipse is vertical ellipse.
Hence $y+1=0$ will be minor axis and $x=1$ will be major axis.