If the tangent at P(θ) on the ellipse 16x2+11y2=256touches the circle  x2+y2+2x−15=0, then θ−

Centre of the circle is (– 1, 0) and radius is 4. Equation of the tangent at P(θ) to the ellipse isx4cos⁡ θ+y16/11sin⁡ θ=1If this touches the circle, then−cos⁡ θ4−1cos2⁡ θ16+sin2⁡ θ256/11=4⇒(cos⁡ θ+4)2=256cos2⁡ θ16+11sin2⁡ θ256⇒4cos2⁡ θ−8cos⁡ θ−5=0⇒(2cos⁡ θ−5)(2cos⁡ θ+1)=0⇒cos⁡ θ=−1/2⇒θ=2π/3