Hi there, I am glad to meet y'all here, I just wanna try this learning website to enhance my knowledge and skills a lot. My Prof. has already been asked these questions. However, I have no idea on this topic. But, Can you assist/tech me about these Problems? I am really appreciate it. Thank you so much??

Can you Analyze and show the computation for the following questions? Then sketch the given equation. Thank you so much ??

2 2 24. Reduce 4y +9x -24y-72x+144=0 to standard form of the equation of an ellipse. Find the coordinates of the center, vertex and foci. Also, find the endpoints and the length of the latera recta, minor axis and major axis. Then, find the equation of the directrices (20 pts.) 2 2 25. Given an equation of hyperbola x -y =1. Find the coordinates of the foci and the endpoints of the transverse axis, 64 36 conjugate axis, central rectangle and the latera recta. Also, find the length of the transverse axis, conjugate axis, and the latera recta. Then, find the equation of the directrices and asymptotes. (22 pts.) 2 2 26. Given an equation of hyperbola 12y -4x +72y+16x+44=0. Reduce the equation into standard form. Then, find the coordinates of the foci and the endpoints of the transverse axis, conjugate axis, central rectangle and the latera recta. Also, find the length of the transverse axis, conjugate axis, and the latera recta, and determine the equation of the directrices and asymptotes. (23 pts.)2 21. The equation of the parabola is y +8x-6y+25=0, Find the coordinates of the vertex, focus, length and endpoints of the latus rectum. Also, find the equation of the directrix. (7pts.) 2 22. The equation of the parabola is x -6x-12y-51=0. Find the coordinates of the vertex, focus, length and endpoints of the latus rectum. Also, find the equation of the directrix. (7pts.) 23. Find the equation of an ellipse with foci at |0,+4 and a vertex at |0,6. Also, find the endpoints and the length of the latera recta, minor axis and major axis. Then, find the equation of the directrices. (15 pts.)