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AP EAMCET202021 Sep 2020Morning ShiftMathematicsCircleActual

A circle passes through the centre of another circle (x^2+y^2-3 x-4 y-1=0 ) and whose centre is ((5,2) ). Then the equation of this circle is.........

Options

  1. A(4 x^2+4 y^2-40 x-16 y+67=0 )
  2. B(3 x^2+3 y^2-40 x-16 y+67=0 )
  3. C(2 x^2+2 y^2-40 x-16 y+67=0 )
  4. D(x^2+y^2-10 x-4 y+67=0 )

Correct answer

A. (4 x^2+4 y^2-40 x-16 y+67=0 )

Step-by-step solution

The centre of the circle (x^2+y^2-3 x-4 y-1=0 ) is (C(3 / 2,2) ), now as it is given that the required circle passes through the point (C(3 / 2,2) ) and having centre ((5,2) ), so radius of required circle is (r= (5- 3 2 )^2+(2-2)^2 = 7 2 ) ( ) Equation of required circle is ( aligned (x-5)^2+(y-2)^2 & = ( 7 2 )^2 4 x^2+4 y^2-40 x-16 y+116 & =49 4 x^2+4 y^2-40 x-16 y+67 & =0 aligned ) Hence, option (a) is correct.

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