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AP EAMCET202018 Sep 2020Evening ShiftMathematicsCircleActual

The circle (x^2+y^2-6 x-10 y+p=0 ) neither intersects nor touch the coordinate axes and the point ((1,4) ) lies inside the circle. Then the range of possible values of ' (p ) ' is

Options

  1. A(23 < p < 25 )
  2. B(25 < p < 29 )
  3. C(21 < p < 23 )
  4. D(12 < p < 21 )

Correct answer

B. (25 < p < 29 )

Step-by-step solution

The equation of given circle is ( array rlrl x^2+y^2-6 x-10 y+p & =0 & (x-3)^2+(y-5)^2 & =34-p array ) ( ) The point ((1,4) ) lies inside the circle, so ( array ll & 1+16-6-40+p 25 (ii) and & r= 34-p 9 (iii) array ) from in equalities Eqs. (i), (ii) and (iii), we get (25 < p < 29 ) Hence, option (b) is correct.

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