Question

The equation of major axis of the ellipse $\frac{(x-1)^2}{9}+\frac{(y-6)^2}{4}=1$ is

• A. $y-2=0$
• B. $y=6$
• C. $x-1=0$
• D. $x=9$

Hint:

The major axis always passes through the centre and lies along the direction of the larger denominator.

Answer 1

The Correct Option is B

Step 1: Concept Identify the orientation of the ellipse by comparing denominators $a^2$ and $b^2$.

Step 2: Meaning $a^2=9$ (under $x$) and $b^2=4$ (under $y$). Since $a > b$, the major axis is horizontal.

Step 3: Analysis For a horizontal major axis, the equation is $y = k$, where $(h,k)$ is the centre.

Step 4: Conclusion The centre is $(1,6)$, so the equation of the major axis is $y=6$. Final Answer: (B)