ustration 7.50 PQ and RS are two perpendicular chord the rectangular hyperbola xy = c². If C is the center of th tangular hyperbola, then find the value of the product o slopes of CP. CO. CR. and CS.

3. Reason Jupiter's gravity changes a spacecraft's path to a hyperbola as it approaches. The focus of the hyperbola nearest the spacecraft's path is the center of Jupiter. The diameter of the planet is 139,822 km. Suppose the path of an approaching spacecraft has an equation with a = 80,000 km and c= 170,000 Km. Assuming the transverse axis.js horizontal, write the equation that models the path of the spacecraft as it approaches Jupiter. What is the distance from the spacecraft to the planet at the vertex of the hyperbola?

Determine the location of the focus and the directrix of the parabola y + 6y – 8x- 23 = 0. O Focus: (-4, -1) Directrix: y = -5 O Focus: (-4, -5) Directrix: y = -1 O Focus: (-6, -3) Directrix: x = -2 Focus: (-4, -3) Directrix: y = -3 O Focus: (-2, -3) Directrix: x = -6

Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse axis 6 and the curve passes through the point (7, -4).