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Most Important Selected Qs for JEE AdvancedMathematicsCircle

The centre of a circle S=0 lies on 2 x-2 y+9=0 and S=0 cuts orthogonally the circle x^2+y^2=4 . Then the circle must pass through the point

Options

  1. A(1,1)
  2. B(-1 / 2,1 / 2)
  3. C(5,5)
  4. D(-4,4)

Correct answer

D. (-4,4)

Step-by-step solution

Let S x^2+y^2+2 g x+2 f y+c=0 it cuts x^2+y^2=4 orthogonally c=4 Moreover -2 g+2 f+9=0( (-g,-f) satisfy the given equation) array ll & S x^2+y^2+2 g x+2 f y+4=0 & x^2+y^2+(2 f+9) x+2 f y+4=0 & (x^2+y^2+9 x+4 )+2 f(x+y)=0 array It is of the form S+ P=0 and hence passes through the intersection of S=0 and P=0 which when solved give (-1 / 2 , 1 / 2),(-4,4) .

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