What type of conic section is represented by | vedclass

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(C) Comparing the given equation with the general form $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$,we get:$a = 13, h = -9, b = 37, g = 1, f = 7, c = -2$.

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(C) Comparing the given equation with the general form $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$,we get:$a = 13, h = -9, b = 37, g = 1, f = 7, c = -2$.First,we calculate the discriminant $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2$:$\Delta = (13)(37)(-2) + 2(7)(1)(-9) - 13(7)^2 - 37(1)^2 - (-2)(-9)^2$$\Delta = -962 - 126 - 637 - 37 + 162 = -1600 
eq 0$.Since $\Delta 
eq 0$,the conic is non-degenerate.Next,we check the condition $h^2 - ab$:$h^2 = (-9)^2 = 81$ and $ab = 13 	imes 37 = 481$.$h^2 - ab = 81 - 481 = -400  0$.Since $\Delta 
eq 0$ and $h^2 - ab < 0$,the equation represents an ellipse.

What type of conic section is represented by the equation $13x^2 - 18xy + 37y^2 + 2x + 14y - 2 = 0$?

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