Trigonometric identities needed for these 2 questions:
(a) cos^2(theta) + sin^2(theta) = 1. With that in mind, cos(theta) = x/a and sin(theta) = y/b. That's how you have (x/a)^2+(y/b)^2 = 1
(a) tan^2(theta) + 1 = sec^2(theta). With that in mind, tan(theta) = x/a and sec(theta) = y/b. Then you have (x/a)^2 + 1 = (y/b)^2.
Good day.