The chord of contact of the tangents drawn from a point on the circle x2+y2=16 with respect to the hyperbola x216-y29=1 always touches a conic whose eccentricity is

A point on x2+y2=16 be p(4cosθ,4sinθ) The chord of contact of p  w.r.t x216−y29=1 is x16⋅4cosθ−y9⋅4sinθ=1⇒xacosθ−ybsinθ=1, where a=4,b=94 is a tangent to the ellipse x2a2+y2b2=1e=5716