Identify the statements which are True.

  • A
    the equation of the director circle of the ellipse, $5x^2 + 9y^2 = 45 $ is $ x^2 + y^2 = 14.$ 
  • B
    $P$  $\&$ $Q $ are the points with eccentric angles $ \theta \& \theta + \alpha $ on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} $ $= 1$ , then the area of the triangle $OPQ$  is independent of $\theta .$ 
  • C
    the point of intersection of any tangent to a parabola & the perpendicular to it from the focus lies on the tangent at the vertex.
  • D
    all of the above  

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  • [JEE MAIN 2022]