Question

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

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

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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