Identify the graph of the nondegenerate conic sections: 4x^2 - 25y^2 - 24x + 250y - 489 = 0.

Identify the graph of the nondegenerate conic sections: $$4x^2 - 25y^2 - 24x + 250y - 489 = 0$$.

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Aniqa O'Neill

Consider the provided equation, $$4x^2 - 25y^2 - 24x + 250y - 489 = 0$$. Compare with the provided equation $$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$$ So, here we get, $$A = 4 \text{ and } C = -25$$
$$AC = 4(-25)$$
$$= -100$$
$$= -100 < 0$$ Because the $$AC < 0$$ Therefore, the greph of the equation is hyperbola.