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Most Important Selected Qs for JEE AdvancedMathematicsParabola

Paragraph: Let S: 4 x^2-4 x-24 y+49=0 is a parabola and S₁=0 represent locus of middle point of chords of parabola S=0 , which passes through origin. L₁ & L₂ are the tangents for S=0 and normals for x^2+y^2=72 On the basis of above informations, answer the following questions: Question: S₁=0 is -

Options

  1. Aan ellipse
  2. Ba circle
  3. Ca parabola whose axis is parallel to y -axis
  4. Da parabola whose axis is parallel to x -axis

Correct answer

C. a parabola whose axis is parallel to y -axis

Step-by-step solution

aligned & 4 x^2-4 x+1=24 y-48 & (2 x-1)^2=24(y-2) & (x- 1 2 )^2=6(y-2) aligned Let mid point is (h, k) so chord is T=S₁ aligned & 4 h x-2(x+h)-12(y+k)+49 & =4 h^2-4 h-24 k+49 aligned as it passes through origin it will satisfy (0,0) aligned & so -2 ~h -12 k =4 ~h ^2-4 ~h -24 k & 4 x ^2-2 x -12 y =0 & or 6 y =2 x ^2- x which is a parabola. aligned

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