The correct options are
A θ=π4
D θ=−π4
Given, equation of ellipse as x26+y22=1(where length of major axis=√6,b=length of minor axis= √2.)
center of ellipse is (0,0) which is parallel to horizontal axis and with eccentricity 'e'.
Point on the ellipse P(√6cosθ,√2sinθ)
Distance from center to point P, OP=2(Given)
⇒√((√6cosθ−0)2+(√2sinθ−0)2)=2
⇒√(6cos2θ+2sin2θ)=2
⇒6cos2θ+2sin2θ=4
⇒3cos2θ+sin2θ=2
⇒2cos2θ+1=2(since cos2θ+sin2θ=1)
⇒cosθ=±1√2
θ=π4or−π4