Question

Graph the hyperbola with equation quantity x plus one squared divided by nine minus the quantity of y plus four squared divided by twenty five = 1

Answer 1

Answer on Question #45117 - Math - Analytic Geometry

Graph the hyperbola with equation quantity $x$ plus one squared divided by nine minus the quantity of $y$ plus four squared divided by twenty five = 1

Solution:

Graph the hyperbola with equation:

$$\frac {(x + 1) ^ {2}}{9} - \frac {(y + 4) ^ {2}}{2 5} = 1$$

Hyperbola has two asymptotes $y = -5/3^{*}(x+1) - 4$ , $y = 5/3^{*}(x+1) - 4$ , and vertices are in points (-4; -4), (2; -4). Hyperbola was drawn using MAPLE 15:

implicitplot([1/9)*(x+1)^2-(1/25)*(y+4)^2 = 1, y = -5/3*(x+1)-4, y = 5/3*(x+1)-4], x = -10..10, y = -20..20, color = [black, blue, blue], legend = ["graph of a hyperbola", "asymptotes of a hyperbola", "asymptotes of a hyperbola", title = "Graph of hyperbola", labels = ["x values", "y values"], labeldirections = ["horizontal", "vertical"], thickness = [2, 1, 1], linestyle = [solid, longdash, longdash], axis = [gridlines = [20, thickness = 1, colour = green, majorlines = 1]])

$$\begin{array}{l} \text{implicit plot} \left( \left[ \frac{(x + 1)^2}{9} - \frac{(y + 4)^2}{25} = 1, y = -\frac{5}{3}(x + 1) - 4, y \right. \right. \\ \left. = \frac{5}{3}(x + 1) - 4 \right], x = -10..10, y = -20..20, \text{color} = [\text{black}, \text{blue}, \\ \text{blue}], \text{legend} = ["\text{graph of a hyperbola}", \\ \text{"asymptotes of a hyperbola", "asymptotes of a hyperbola", title} \\ = \text{"Graph of hyperbola", labels} = ["\text{x values", "y values"],} \\ \text{label directions} = ["\text{horizontal", "vertical"], thickness} = [2, 1, 1], \\ \text{linestyle} = [\text{solid}, \text{longdash}, \text{longdash}], \text{axis} = [\text{gridlines} = [20, \\ \text{thickness} = 1, \text{colour} = \text{green}, \text{majorlines} = 1]]) \end{array}$$

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