Answer:
1. x^2 y^2
----------- + ----------- = 1
736^2 1467^2
2. 2PQ = <-16,2> magnitude =sqrt(260)
3.The center is (0,0)
The vertices are at (0,±25)
The foci are at (0, ±20)
Step-by-step explanation:
1. Equation for an ellipse
x^2/a^2+ y^2/b^2 = 1
a is the distance from the center to the ellipse
a = the radius of the moon plus the shorter distance of the satellites orbit
a = 567+ 169
=736
b =the radius of the moon plus the longer distance of the satellites orbit
b = 567+ 900
b =1467
x^2 y^2
----------- + ----------- = 1
736^2 1467^2
2. P( -5,5) Q (-13,6)
PQ = Q-P
= (-13--5, 6-5)
= (-13+5,1)
= (-8,1)
2 PQ = 2* (-8,1)
= (-16,2)
magnitude = sqrt((-16)^2 +2^2)
= sqrt(256+4)
=sqrt(260)
3. x^2/225 + y^2/625 = 1
is of the form (x-h)^2/a^2 + (y-k)^2/b^2 =1
where (h,k) is the center
The center is (0,0)
The vertices are at (±b,0) since b>a
sqrt(b^2) = sqrt(625) = 25
The vertices are at (0,±25)
The foci are at (0, ±c)
where b^2= a^2 +c^2
625^2 = 225+c^2
Subtract 225 from each side
400 = c^2
sqrt(c^2) = sqrt(400)
c = 20
The foci are at (0, ±20)
