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Most Important Selected Qs for JEE AdvancedMathematicsCircle

Let a and b be two real numbers such that a^2-3 b^2+4 a+1=0 . If the line a x+b y+1=0 touches a fixed circle A and b , then which of the following is/are correct?

Options

  1. ACentre of the circle is (2,0)
  2. BRadius of the circle is 3
  3. CCircle is passing through (2,3)
  4. DRadius of the circle is 3

Correct answer

B. Radius of the circle is 3

Step-by-step solution

aligned & 4 a^2+4 a+1=3 b^2+3 a^2 & (2 a+0 b+1)^2 a^2+b^2 = 3 ^2 aligned Centre of the circle is (2,0) , radius is 3 .

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