5. [-/0.12 Points] DETAILS SCALCET9 10.5.011. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find the vertices and foci of the ellipse. x2 yz 16 25 = 1 vertices ( x, y ) = (smaller y-value) ( x, y ) = (larger y-value) foci ( x, y ) = (smaller y-value) ( x, y ) = (larger y-value) Sketch its graph. 4 -6 -4 6 -6 - 2 - 2 O - 6 21 -6 -2 6 -6 -4 2 -2 -4 O OO Need Help? Read It Watch It 6. [-/0.12 Points] DETAILS SCALCET9 10.5.018. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following 2 -2 -1 1 2 3 Find an equation of the ellipse. Find its foci. smaller x-value ( x, y ) = larger x-value ( x, y ) = Need Help? Read It1. [-/0.12 Points] DETAILS SCALCET9 10.5.AE.003. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Example Video Example () Find the equation of the ellipse with foci (0, +3) and vertices (0, +4). Solution Using the standard notation, we have c = [ and a =. Then we obtain b2 = a2 - c2 = 16 - = ), so an equation of the ellipse is x 2 = 1. Another way of writing this equation is 16x2 + 7y2 =. Need Help? Read It 2. [-/0.12 Points ] DETAILS SCALCET9 10.5.AE.007. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Example Video Example () Sketch the conic below and find its foci. 36x2 - 25y - 288x + 150y + 1,251 = 0 Solution 15 10 5 X -4 -2 2 4 10 - 10 We complete the squares as follows. 25(y2 - 6y) - 36(x2 - 8x) = 1,251 25 ( 12 - 6y + - 36 (x2 - 8x + = 1, 251+ 225 - 576 25 (x - ) 2 - 36 ( x - ) ? = 0 ( *- O) (x- O ) . . This is in the standard form except that x and y are replaced by x - 4 and y - 3. Thus a2 = , 62 = ], and c2 =. The hyperbola is shifted four units to the right and three units upward. The foci are (x, y) = and (4, 3 - V61) and the vertices are (x, y) = and ( 4 , - 3 ) . The asymptotes are y - 3 = + - (x - 4). The hyperbola is sketched in the figure above. Need Help? Read It14. [-/0.12 Points] DETAILS SCALCET9 10.5.052. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER A cross-section of a parabolic reflector is shown in the figure. The bulb is located at the focus and the opening at the focus is 6 cm. V X B D (a) Find an equation of the parabola. (b) Find the diameter of the opening |CD|, 19 cm from the vertex. cm Need Help? Read It9. [-/0.12 Points] DETAILS SCALCET9 10.5.036. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find an equation for the conic that satisfies the given conditions. parabola, focus (2, -3), vertex (2, 6) Need Help? Read It 10. [-/0.12 Points] DETAILS SCALCET9 10.5.035. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find an equation for the conic that satisfies the given conditions. parabola, focus (-4, 0), directrix x = 0 Need Help? Read It Watch It 11. [-/0.12 Points] DETAILS SCALCET9 10.5.041. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find an equation for the conic that satisfies the given conditions. ellipse, foci (0, 1), (0, 5), vertices (0, 0), (0, 6) Need Help? Read It Watch It 12. [-/0.12 Points] DETAILS SCALCET9 10.5.045. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find an equation for the conic that satisfies the given conditions. hyperbola, vertices (12, 0), foci (+5, 0) Need Help? Read It Watch It 13. [-/0.12 Points] DETAILS SCALCET9 10.5.047. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find an equation for the conic that satisfies the given conditions. hyperbola, vertices (-1, -3), (-1, 5), foci (-1, -6), (-1, 8) Need Help? Read It Watch It3. [-/0.12 Points] DETAILS SCALCET9 10.5.004. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find the vertex, focus, and directrix of the parabola. 5x2+ 12y = 0 vertex ( x, y ) = focus ( x, y ) = directrix Sketch its graph. 4 2 2 X -6 -4 -2 2 - 2 2 -2 L2 O -4 N 4 4 -2 2 -21 -4 =2_ -2 O Need Help? Read It 4. [-/0.12 Points] DETAILS SCALCET9 10.5.010.MI. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following. N -1 2 3 -2 -3 Find an equation of the parabola. Find the focus and directrix. focus ( x, y) = directrix Need Help? Read It Master It7. [-/0.12 Points] DETAILS SCALCET9 10.5.021. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find the vertices and foci of the hyperbola. y2 - x2 = 36 vertices (x, y) = (smaller y-value) ( x, y ) = (larger y-value) foci ( x, y ) = (smaller y-value) ( x, y) = (larger y-value) Find the asymptotes of the hyperbola. (Enter your answers as a comma-separated list of equations.) Sketch its graph. 15 20 10 10 X -20 -10 10 20 -15 -10 -5 5 10 15 -5 - 10 -10 -20 O -15 D 15 15 10 10 5 5 -15 -10 -5 5 10 15 -15 -10 5 10 15 -5 -5/ -10 10 -15 -15 O Need Help? Read It Watch It 8. [-/0.12 Points] DETAILS SCALCET9 10.5.029. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Identify the type of conic section whose equation is given. x2 = 4y - 2y2 O parabola O ellipse O hyperbola Find the vertices and foci. vertices (x, y) = (smaller x-value) (x, y) = (larger x-value) foci (x, y) = ( (smaller x-value) ( x, y ) = (larger x-value) Need Help? Read It