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Most Important Selected Qs for JEE AdvancedMathematicsCircle

If a variable line L: 3 x-2 y-4+ (x-2 y+4)=0 where is a parameter is passing through a fixed point P(a, b) and S: x^2+y^2=8 is a circle, then: ( array |c|l|c|c| & List-I & & List-II (P) & (a+b) is equal to & (1) & 2 2 (Q) & Length of the tangent from 'P' to the circle 'S' is & (2) & 4 2 ( R ) & Least distance of 'P' to the circle 'S' is & (3) & 6 2 ( S ) & array l Least radius of the circle whose centre is 'P' and it

Options

  1. AP 5 ; Q 2 ; R 2 ; S 4
  2. BP 5 ; Q 4 ; R 1 ; S 3
  3. CP 5 ; Q 4 ; R 3 ; S 3
  4. DP 5 ; Q 2 ; R 2 ; S 4

Correct answer

B. P 5 ; Q 4 ; R 1 ; S 3

Step-by-step solution

aligned & L : 3 x-2 y-4+ (x-2 y+4)=0 & P(a, b) (4,4) & S : x^2+y^2=8 aligned (P) a+b=8 (Q) L_T= S₁ = 16+16-8 =2 6 (R) Least distance =O P-r=4 2 -2 2 =2 2 (S) Least radius of the circle containing the given circle is =O P+r=4 2 +2 2 =6 2

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