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Q.
The centre of the ellipse
$9x^{2} + 2 5y^{2} - 18x- 100y - 116 = 0$ is
Conic Sections
Solution:
Given equation of ellipse is
$9 x^{2}+25y^{2}-18x-100y-116=0$
$\Rightarrow 9\left(x^{2}-2x\right)+25\left(y^{2}-4y\right)-116=0$
$\Rightarrow 9\left(x^{2}-2x+1\right)+25\left(y^{2}-4y+4\right)-100-9-116=0$
$\Rightarrow 9\left(x-1\right)^{2}+25\left(y-2\right)^{2}=225$
$\therefore $ Centre $\left(1,2\right)$.