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Most Important Selected Qs for JEE AdvancedMathematicsEllipse

If the normal at any given point P on ellipse x^2 a^2 + y^2 b^2 =1 meets its auxiliary circle at Q and R such that QOR =90^ , where O is centre of ellipse, then

Options

  1. A2 (a^2-b^2 )^2=a^4 ^2 +a^2 b^2 cosec ^2
  2. Ba^4+5 a^2 b^2+2 b^4=a^4 ^2 +a^2 b^2 ^2
  3. Ca^4+5 b^2 a^2+2 b^4 2 a^3 b
  4. Da^4+2 b^4 5 a^2 b^2+2 a^3 b

Correct answer

D. a^4+2 b^4 5 a^2 b^2+2 a^3 b

Step-by-step solution

Homogenizing auxiliary circle with normal at Px^2+y^2= a^2(a x -b y cosec )^2 (a^2-b^2 )^2 Q O R=90^ -1+ a^4 ^2 (a^2-b^2 )^2 -1+ a^2 b^2 cosec ^2 (a^2-b^2 )^2 =02 (a^2-b^2 )^2=a^4 ^2 +a^2 b^2 cosec ^2 ^4-5 a^2 b^2+2 b^4=a^4 ^2 +a^2 b^2 ^2 2 a^3 b

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