PROBLEM INVOLVING ELLIPSE | PLEASE PROVIDE CLEAR STEP-BY-STEP SOLUTION AND EXPLANATION SO THAT I CAN USE THIS AS MY GUIDE, THANKYOU SO MUCH

a. Find the Standard equation of the given ellipse.

Use the information below to find the standard equation of the given ellipse. 1. foci (-3, 0), and (3, 0), contains the point (4,1)2. foci(-7, 8) and (-7, -6), the sum of distances of any point from the foci is 2157\fGiven the equation of the ellipse below, find the center, foci, vertices and covertices. Then, sketch the graph and indicate the center. 1. 25x2 + 169y2 = 42252. 25x2 - 200x + 16y2 -160y + 400 = 0