Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Horizontal axis and passes through the point (-6, 7) Submit Answer 3. [-/6.66 Points] DETAILS MY NOTES LARPCALC11 10.2.031. Find the standard form of the equation of the parabola with the given characteristics. Vertex: (0, 9); directrix: y = 13 Submit Answer 4. [-/6.66 Points] DETAILS MY NOTED LARPCALC11 10.3.011. Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (+5, 0); foci: (+4, 0)Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. 4 10/ 5- Focus (-3.5, 0) X -5 5 -5F -101 (iFind the center, vertices, foci, and eccentricity of the ellipse. 4x2 + y2 = 16 Center: (x, y) = Vertices: smaller y-value (x, y) = larger y-value ( x, y ) = Foci: smaller y-value (x, y) = larger y-value (x, y ) = Eccentricity : Sketch the ellipse.Find the center, vertices, foci, and eccentricity of the ellipse. 12x2 + 24y2 - 12x + 48y - 45 = 0 Center: (x, y) = Vertices: smaller x-value (x, y) = larger x-value (x, y ) = Foci: smaller x-value (x, y) = larger x-value ( x, y ) = Eccentricity: Sketch the ellipse.Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (0, +3); foci: (0, +6)Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) 9x2 - y2 + 18x + 6y - 9=0 Center: (x, y) = Vertices: smaller x-value (x, y ) = larger x-value ( x, y) = Foci: smaller x-value (x, y) = larger x-value (x, y) = Asymptotes: negative slope positive slope Sketch the hyperbola using the asymptotes as an aid.Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form. (Use xp for x' and yp for y' in your answer. Rotate the coordinate axes through an angle 0 with O S O S T/ 2. ) xy - 9 = 0 Sketch the graph of the resulting equation, showing both sets of axes. 103 103 107 yp yp N -10 -8 6 -4 -10 8 6 -4 2 4 6 8 10 -10 -8 6 -4 -2 2 10 -10 -8 -6 -4 -2 2 6 -2- -2- -2- 4 46- Maple Generated Plot -10- -163Consider the parametric equations x = 9 cos(0) 2 and y = 3 sin(0). (a) Create a table of x- and y-values using 0 = - 0, and 2 4 4 2 A N 0 NA X (b) Plot the points (x, y) generated in part (a), and sketch a graph of the parametric equations. yA point is given in rectangular coordinates. Convert the point to polar coordinates. (There are many correct answers.) (-3, 0) R |) 13. [-/6.66 Points] DETAILS MY NOTES LARPCALC11 10.7.074. Convert the rectangular equation to polar form. Assume a > 0. x2+y25ay=0 | Submit Answer | | | | | | | 14. [-/6.66 Points] DETAILS MY NOTES LARPCALC11 10.7.087. ' Convert the polar equation to rectangular form. | i\\ r? = cos(6)