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Question

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


A
(0,0)
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B
(1,0)
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C
(0,1)
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D
(1,1)
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Solution

The correct option is B $$(1,1)$$
Centre of the ellipse is the intersection point of 

$$x+y-2=0.........(1)$$ 
 $$x-y=0............(2)$$

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.

Mathematics

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