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  • The centre of the ellipse <img alt="\mathrm{14 x^2-4 x y+11 y^2-44 x-58 y+71=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B14%20x%5E2-4%20x%20y&plus;11%20y%5E2-44%20

The centre of the ellipse \mathrm{14 x^2-4 x y+11 y^2-44 x-58 y+71=0} is

Option: 1

(-2,3)


Option: 2

(2,-3)


Option: 3

(2,3)


Option: 4

(-2,-3)


Answers (1)

best_answer

Let  \mathrm{\mathrm{S} \equiv 14 x^2-4 x y+11 y^2-44 x-58 y+71=0}

For finding center of any conic differentiate first with respect of X, then with

respect of Y, we get two liner quations in X and Y. On solving them we get 

center of the conic.

              \mathrm{\begin{aligned} & \frac{\partial S}{\partial x}=28 x-4 y-44=0 \\ & \frac{\partial S}{\partial y}=-4 x+22 y-58=0 \end{aligned}} 

On solving, we get X=2 , Y=3. 

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