5. ¿Cuál es la ecuación de la circunferencia de centro en el origen y que pasa por el punto \( (2,-3) \) 6. Encuentra la ecuación de la circunferencia de diámetro el segmento formado por los puntos,

Calculate the slope for the line given by the points \((-1, -4)\) and \((4, 2)\).

A cone has a radius of 3 cm and a height of 5 cm. What is its volume?

Describe the relationship between a secant and a tangent line at the point of contact with a circle.

14. The actual area of a park is \( 0.08 \mathrm{~km}^{2} \). If the area of the park on a map is \( 32 \mathrm{~cm}^{2} \), then the scale of the map is A. \( 1: 250 \). B. \( 1: 5000 \). C. \( 1: 40000 \). B. \( 1: 25000000 \).

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 y-axis. The vertices are at \( (-3,6),(-3,2) \). (Type an ordered pair. Use a comma to separate answers as needed.) The foci are at \( (-3,4+\sqrt{5}),(-3,4-\sqrt{5}) \). (Simplify your answer. Type an ordered pair. Type an exact answer, using radicals as needed. Use as needed.) The asymptotes are \( \square= \pm(\square) \). (Simplify your answers. Use integers or fractions for any numbers in the expressions.)