Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints of transverse axis: \( (0,-8),(0,8) \); asymptote: \( y=2 x \) The equation is

Find the center, transverse axis, vertices, foci, and asymptotes. Graph the equation. \( y^{2}-25 x^{2}-100 x-2 y-124=0 \) The center of the hyperbola is at \( (-2,1) \). (Type an ordered pair.) The transverse axis is parallel to the

Below is the graph of \( y=x^{3} \) Transform it to make it the graph of \( y=-2(x-4)^{3} \)

Find the standard form of the equation of the hyperbola satisfying the given conditions. Center: \( (4,-2) \); focus: \( (8,-2) \); vertex: \( (7,-2) \) The equation is

Find the center, transverse axis, vertices, foci, and asymptotes. Graph the equation. \[ y^{2}-4 x^{2}-24 x-8 y-24=0 \] The center of the hyperbola is at \( (-3,4) \). (Type an ordered pair.) The transverse axis is parallel to the

Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints of transverse axis: \( (0,-8),(0,8) \); asymptote: \( y=2 x \) The equation is