Tangent to ellipse also tangent to circle

  • #1

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
 

Answers and Replies

  • #2
35,268
11,534
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.
 

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