The straight line x+y=a will be a tangent to the ellipse x^2/9+y^2/16=1,if a is

1.8
2.+or-5
3.+or-10
4.+or-6

Any tangent to the ellipse x^2/9+y^2/16=1 is
y=mx(+or-)sqrt(9m^2+16) [y=mx(+or-)sqrt(a^2m^2+b^2)]
when m=-1 (slope of given line=-1)
the equation becomes
y=-x(+or-)sqrt(9+16)
x+y=+or-5
a=+or-5

y=-x+a m=-1, c=a a^2=9, b^2=16 a^2
c^2=b^2m^2-a^2 a^2=16+9=25, a=+or- 5

2.+or-5