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AP EAMCET20227 Jul 2022Morning ShiftMathematicsCircleActual

Suppose d₁ and d₂ are respectively the lengths of intercepts of the cirlce x^2+y^2=4 and x^2+y^2-10 x-14 y+65=0 on the line 2 x-2 y-3=0 . Then, which of the following is true?

Options

  1. Ad₁=2 d₂
  2. Bd₂=2 d₁
  3. Cd₁=3 d₂
  4. Dd₁=d₂

Correct answer

D. d₁=d₂

Step-by-step solution

aligned & O A= |0-0-3| 2^2+2^2 = 3 8 & A B= 2^2- ( 3 8 )^2 = 4- 9 8 = 23 8 aligned d₁=2 23 8 x^2+y^2-10 x-14 y+65=0 gathered g=-5, f=-7, c=65 r= 25+44-65 =3 gathered P Q= |2 5-2 7-3| 2^2+2^2 = 7 8 Q R= 3^2- ( 7 2 )^2 = 23 8 d₂=2 Q R d₂=2 23 8 d₁=d₂

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