find the coordinate of the center and identify the conic:

Question

5y^2 - 2x^2 - 10y - 12x = 23

Answer 1

Complete the squares of each squared term:
5y^2 - 2x^2 - 10y - 12x = 23
5(y-1)^2-5 -2(x+3)^2+18 = 23
5(y-1)^2 -2(x+3)^2 = 10

((y-1)/sqrt(2))^2 -((x+3)/sqrt(5))^2=1

From the above, the centre is located at (-3,1) and it is a hyperbola expressed in the form ((x/a)^2-(y/b)^2=1).

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