Question: Please show all steps. 1. The equation y^2 - 4y - 4x^2 +13 = 0 will produce a hyperbola. How can we tell by simply

Please show all steps.

1. The equation y^2 - 4y - 4x^2 +13 = 0 will produce a hyperbola. How can we tell by simply observing the equation? In what directions do the branches of this hyperbola open? How do you know? Explain. Sketch a graph of this hyperbola, clearly indicating how you have determined the key characteristics (center, vertices, eccentricity, foci). Give the domain and range of this hyperbola.

2. Find the standard form of the equation of the ellipse satisfying the following conditions: endpoints of the major axis (-5, 4) and (3, 4); endpoints of minor axis (-1, 1) and (-1, 7). Graph this conic, marking the center and vertices.

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