Tangent to ellipse also tangent to circle

[sarthak sharma]

Homework Statement

if the tangent at a point P("theta") on the ellipse

16 (x^2) + 11 (y^2) = 256​

is also tangent to the circle

(x^2) + (y^2) + 2(x) = 15​

then ("theta") = ??

2. The attempt at a solution

{{{{ i have taken "theta" as "d" }}}}​

P [4 cos d , (16/(sqrt11)) sin d]

equation of tangent at P on ellipse is {(cos d) / 4] x + [(sin d) / (16/(sqrt11))] y = 1 .....(i)

centre of given circle C(-1,0) and radius r = 4

for (i) to also be tangent on the circle - perpendicular distance of (i) from C must be equal to 4

but when i tried to do so i could not get the answer
may be I am doing something wrong so please anyone could guide me the correct way

 

[mfb]

but when i tried to do so i could not get the answer

The approach looks good, so please show your work so we can see what went wrong.