6. [6/7 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 11.3.010.MI. MY NOTES ASK YOUR TEACHER An equation of a hyperbola is given. = 1 16 (a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a comma-separated list of equations.) vertex ( x, y) = 0, - 3 (smaller y-value) vertex (x, y) = |0,3 (larger y-value) focus (x, y) = 10, -5 (smaller y-value) focus (x, y) = 0,5 (larger y-value) y= 3x 3x asymptotes 4'4 (b) Determine the length of the transverse axis. (c) Sketch a graph of the hyperbola. y 4 15 15/ 10 1017. [6/7 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 11.3.017.MI. MY NOTES ASK YOUR TEACHER An equation of a hyperbola is given. 25x2 - 16y2 = 400 (a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a comma-separated list of equations.) vertex ( x, y ) = ( -4,0 (smaller x-value) vertex ( x , y ) = 4.0 (larger x-value) focus ( x, y) = ( -V41,0 (smaller x-value) focus (x, y) = ( V41,0 (larger x-value) 5x 5x asymptotes V= 4 4 (b) Determine the length of the transverse axis. (c) Sketch a graph of the hyperbola. y 4 10/ 10/8. [-/1 Points] DETAILS SPRECALC7 11.3.028.MI. MY NOTES ASK YOUR TEACHER Find the equation for the hyperbola whose graph is shown. 4 10/ F1 (0, 5) X -10 -5 10 F2 (0, -5) -10 Show My Work (Optional) ?9. [-/1 Points] DETAILS SPRECALC7 11.3.032. MY NOTES ASK YOUR TEACHER Find the equation for the hyperbola whose graph is shown. 4 10 5 WIH - X y= X -10 10 -5 -10 Show My Work (Optional) ?11. [-/1 Points] DETAILS SPRECALC7 11.3.038.MI. MY NOTES ASK YOUR TEACH Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, +9), vertices: (0, +3) Show My Work (Optional) 12. [-/1 Points] DETAILS SPRECALC7 11.3.042.MI. MY NOTES ASK YOUR TEACH Find an equation for the hyperbola that satisfies the given conditions. Vertices: (0, #7), asymptotes: y = + x + Show My Work (Optional)13. [-/1 Points] DETAILS SPRECALC7 11.3.044. MY NOTES ASK YOUR TEACH Find an equation for the hyperbola that satisfies the given conditions. Vertices ($5, 0), hyperbola passes through (6, v 66) Show My Work (Optional) ? 14. [-/1 Points] DETAILS SPRECALC7 11.3.050.MI. MY NOTES ASK YOUR TEACH Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, +7), length of transverse axis: 7 # Show My Work (Optional)15. [2/9 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 11.3.051. MY NOTES ASK YOUR TEACH (a) Show that the asymptotes of the hyperbola x2 - y2 = 3 are perpendicular to each other. We first write the equation x2 - y2 = 3 in standard form, 62 5 = 1. * 2 3 3 : 1 Therefore, we have the following. a X b= X Thus, the asymptotes are y = + X and the slopes of the asymptotes are m1 = J X (smaller value) m2 = X (larger value) Since m1 . m2 = X we see that the asymptotes are perpendicular to each other. (b) Find an equation for the hyperbola with foci (x, y) = (+c, 0) and with asymptotes perpendicular to each other.Submit Answer 16. [-/2 Points] DETAILS SPRECALC7 11.3.057.MI. MY NOTES ASK YOUR TEACH Some comets, such as Halley's comet, are a permanent part of the solar system, traveling in elliptical orbits around the sun. Other comets pass through the solar system only once, following a hyperbolic path with the sun at a focus. figure shows the path of such a comet. Find an equation for the path, assuming that the closest the comet comes to the sun is 4 x 109 mi and that the path the comet was taking before it neared the solar system is at a right angle to the path it continues on after leaving solar system. (Round your answers to two decimal places.) x2 - y2 = x 10 # Show My Work (Optional)22. [-/1 Points] DETAILS SPRECALC7 11.4.034. MY NOTES ASK YOUR TEACHE Find an equation for the conic whose graph is shown. y 15/ 10 -10 -5 5 10 15 -10 -15 Show My Work (Optional)23. [-/1 Points] DETAILS SPRECALC7 11.4.037. MY NOTES ASK YOUR TEACHE Find an equation for the conic section with the given properties. The hyperbola with center C(-1, 3), vertices Vi(-1, -3) and V2(-1, 9), and foci F1(-1, -4) and F2(-1, 10) # Show My Work (Optional) 24. [-/1 Points] DETAILS SPRECALC7 11.4.042. MY NOTES ASK YOUR TEACHE Find an equation for the conic section with the given properties. The hyperbola with foci F1(-2, 3) and F2(6, 3) that passes through the point (5, 3) Show My Work (Optional)25. [7/11 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 11.4.050. MY NOTES ASK YOUR TEACHE Complete the square to determine whether the graph of the equation is an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. x2 + 4x + 12y+4 = 0 O ellipse O parabola O hyperbola O degenerate conic O no solution If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the focus, vertex, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. (Enter your answers for asymptotes as a comma-separated list of equations. If an answer does not exist, enter DNE.) center (x, y) = DNE focus ( x, y ) = (smaller x-value or only focus) X ca focus ( x, y ) = (larger x-value) + X vertex (x, y) = ( (smaller x-value or only vertex) X X vertex ( x, y ) = (larger x-value) X VO O! length of the major axis DNE length of the minor axis DNE asymptotes DNE26. [8/11 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 11.4.051. MY NOTES ASK YOUR TEACHE Complete the square to determine whether the graph of the equation is an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. 4x2 + 25y2 - 32x + 250y + 589 = 0 O ellipse O parabola O hyperbola O degenerate conic O no solution If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the focus, vertex, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. (Enter your answers for asymptotes as a comma-separated list of equations. If an answer does not exist, enter DNE.) center ( x, y ) = 4, - 5 focus (x, y) = 4- V21, -5 (smaller x-value or only focus) focus (x, y) = ( 4+V21, -5 (larger x-value) vertex ( x, y ) = (smaller x-value or only vertex) X vertex (x, y) = ( 9, -5 (larger x-value) length of the major axis X length of the minor axis X asymptotes DNE26. [8/11 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 11.4.051. MY NOTES ASK YOUR TEAC - Complete the square to determine whether the graph of the equation is an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. 4x2 + 25y2 - 32x + 250y + 589 = 0 O ellipse O parabola O hyperbola O degenerate conic O no solution If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the focus, vertex, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. (Enter your answers for asymptotes as a comma-separated list of equations. If an answer does not exist, enter DNE.) center ( x, y ) = 4, - 5 focus (x, y) = 4- V21, -5 (smaller x-value or only focus) focus (x, y) = 4+V21, -5 (larger x-value) vertex ( x , y ) = (smaller x-value or only vertex) X vertex (x, y) = ( 9, - 5 (larger x-value) length of the major axis X length of the minor axis X asymptotes DNE27. [9/11 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 11.4.053. MY NOTES ASK YOUR TEACHER Complete the square to determine whether the graph of the equation is an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. 16x2 - 9y2 - 160x + 544 = 0 O ellipse parabola O hyperbola O degenerate conic O no solution If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the focus, vertex, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. (Enter your answers for asymptotes as a comma-separated list of equations. If an answer does not exist, enter DNE.) center (x, y) = 15,0 focus ( x, y ) = ( 5, -5 (smaller y-value or only focus) focus (x, y) = 5,5 (larger y-value) vertex (x, y) = ( ] 5, - 4 (smaller y-value or only vertex) vertex (x, y ) = ( 5,4 (larger y-value) length of the major axis length of the minor axis 20 asymptotes 3 3 3 + 20