(a) The poins the are O(0,0) , P (3,4) and Q(6,8). Then
`2a=PO+OQ`
`5+10=15`
or `a=(15)/(2)`
Also, the distance between the foci,
`2ae=(sqrt(6-3)^(2)+(8-4)^(2))=5`
or `e=(1)/(3)`
`or b^(2)=(225)/(4)(1-(1)/(9))=50`
`b=5sqrt(2)`
`2b=10sqrt(2)`
(b) We know that
`(1)/(SP)+(1)/(SQ)=(2a)/(16)`
or SQ=8
or PQ=10
(c) If the line `x=x+k` touches the ellipse o`9x^(2)+16y^(2)=144` then,
or `k=+-5`
(d) The sum of the distance of a point of the ellipe from the foci is 2a=8
