Question

The centre of the ellipse $\frac{{(x+y-2)}^2}{9}+\frac{{(x-y)}^2}{16}=1$ is

• A. $(0,0)$
• B. $(1,0)$
• C. $(0,1)$
• D. $(1,1)$

Answer 1

Answer: (D)

$(1,1)$

Centre of the ellipse is the intersection point of

$x+y-2=\mathrm{0.........}\left(1\right)$

$x-y=\mathrm{0............}\left(2\right)$

Subsituting $x$ from equation $2$ in equation $1$ two equations, we get,

$2y=2$

$y=1$

Replacing, we get $x=1$

$\Rightarrow (1,1)$ is the centre.