重酬!!! SUPER EASY MATHS (超趕ga)

Q1) An ellipse has centre at the origin and foci on the x-axis. If itpasses through
the points (5，1) and (－4，－2)，find itsequation.
Sol
x^2/a^2+y^2/b^2=1，a>b>0
25/a^2+1/b^2=1，16/a^2+4/b^2=1
4*(25/a^2+1/b^2)-(16/a^2+4/b^2)=4-1
84/a^2= 3
a^2=28
25/28+1/b^2=1
1/b^2=3/28
x^2/28+3y^2/28=1
x^2+3y^2=28

Q2) Anellipse has same foci as the ellipse x^2 / 16 + y^2 / 4 = 1 and it passesthrough
the point P (√5,-√6).Find the equation of the ellipse.
Sol
x^2/a^2+y^2/(a^2－12)=1，a^2>12
5/a^2+6/(a^2－12)=1
5(a^2－12)+ 6a ^2=a^2(a^2－12)
11a^2－60=a^4－12a^ 2
a^4 -23a ^2+60=0
(a^2－3)(a^2－20)= 0
a^2=3(reject) or a^2=20
x^2/20+y^2/8=1

I have a few questions on your answers...

Q1)

4*(25/a^2+1/b^2)-(16/a^2+4/b^2)=4-1

i don't understand this step....why need to time 4??
please explain briefly.

Q2)

why need to let b be a^2-12 ??
why a^2>12 ??
Please tell me briefly!! =]