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Most Important Selected Qs for JEE AdvancedMathematicsEllipse

Paragraph: An ellipse whose major axis is parallel to x -axis such that segment of a focal chord are 1 and 2 units. The line x a + y b + 1 c =0 are the chords of the ellipse such that a, c, b are in H.P. and are bisected by the point at which they are concurrent, the equation of auxiliary circle is 2 x^2+2 y^2+4 p x+4 q y-16 p+1=0 then Question: Equation of director circle is

Options

  1. Ax ^2+ y ^2- x - y - 37 6 =0
  2. Bx^2+y^2+x+y+ 37 6 =0
  3. Cx^2+y^2+x+y- 37 6 =0
  4. Dx^2+b^2-x-y+ 37 6 =0

Correct answer

C. x^2+y^2+x+y- 37 6 =0

Step-by-step solution

a , c , b are in H.P. 2 c = 1 a + 1 b Line x a + y b + 1 c =0 passes through a fixed point (- 1 2 ,- 1 2 ) So centre of ellipse is (- 1 2 ,- 1 2 ) Which is also centre of auxiliary circle p = 1 2 , q = 1 2 radius of auxiliary circle =2 Length of major axis =4 also it segment of focal chord are 1,2 1 1 + 1 2 = 4 b^2 b^2= 8 3 Director circle (x+ 1 2 )^2+ (y+ 1 2 )^2= 8 3 +4

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