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Most Important Selected Qs for JEE AdvancedMathematicsParabola

Paragraph: A variable circle passes through the point A(2,1) and touches the x -axis. Locus of the other end of the diameter through A is a parabola. Question: The length of the latus rectum of the parabola, is

Options

  1. A1
  2. B2
  3. C4
  4. D8

Correct answer

C. 4

Step-by-step solution

(i) Equation of the variable circles gathered (x-h)(x-2)+(y-k)(y-1)=0 x^2+y^2-(2+h) x-(k+1) y+k+2 h=0 gathered As x -intercept =0 aligned & g ^2= c & ( ~h +2)^2 4 = k +2 ~h & ( ~h +2)^2=4 k +8 ~h & ( ~h -2)^2=4 k aligned Locus is (x-2)^2=4 y L.R. =4 Ans. (ii) N (2,-1) Ans. (iii) Figure is a square. Area = (4)(4) 2 =8 sq. units Ans.

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