AP EAMCET202421 May 2024Morning ShiftMathematicsCircleActual

If (a, b) is the midpoint of the chord 2 x-y+3=0 of the circle x^2+y^2+6 x-4 y+4=0 , then 2 a+3 b=

Options

Correct answer

C. 1

Step-by-step solution

aligned & 2 x-y+3=0, y=2 x+3 & x^2+y^2+6 x-4 y+4=0 & x^2+(2 x+3)^2+6 x-4(2 x+3)+4=0 & 5 x^2+10 x+1=0 aligned Sum of roots x₁+x₂=- 10 5 =-2 Mid point ( x₁+x₂ 2 , y₁+y₂ 2 )= ( -2 2 , x₁+x₂+3 )(a, b)=(-1,1) 2 a+3 b=1

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