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Paragraph: Tangents are drawn from a variable point P to the ellipse x^2+4 y^2=4 meeting it at Q & R . So Q R is chord of contact of pair of tangents drawn from P . On the basis of above information answer the following : Question: If angle between PQ & PR is 45^ , then locus of P is -

Options

  1. A(x^2+y^2-5 )=4 (x^2+4 y^2-4 )^2
  2. B(x^2+y^2-5 )^2=4 (x^2+4 y^2-4 )
  3. C(x^2+y^2-4 )=5 (x^2+4 y^2-4 )^2
  4. Dx^2+4 y^2=5

Correct answer

B. (x^2+y^2-5 )^2=4 (x^2+4 y^2-4 )

Step-by-step solution

aligned & 45^ = | m₁-m₂ 1+m₁ m₂ | & (1+ m ₁ ~m ₂ )^2= ( m ₁+ m ₂ )^2-4 ~m ₁ ~m ₂ & (1+ k ^2-1 ~h ^2-4 )^2= ( 2 hk h ^2-4 )^2-4 k ^2-1 ~h ^2-4 & ( x ^2+ y ^2-5 )^2=4 [ x ^2 y ^2- ( y ^2-1 ) ( x ^2-4 ) ] & ( x ^2+ y ^2-5 )^2=4 [4 y ^2+ x ^2-4 ] aligned

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