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AP EAMCET202021 Sep 2020Evening ShiftMathematicsCircleActual

If the point ((1,4) ) lies inside the circle (x^2+y^2-6 x-10 y+p=0 ) and the circle does not touch or intersect the coordinates axes, then

Options

  1. A(0 < p < 34 )
  2. B(25 < p < 29 )
  3. C(9 < p < 25 )
  4. D(7 < p < 29 )

Correct answer

B. (25 < p < 29 )

Step-by-step solution

Equation of given circle ( array rlrl & x^2+y^2-6 x-10 y+p & =0 & (x-3)^2+(y-5)^2 & =34-p & 34-p > 0 p 25 (ii) and 34-P 9 (iii) array ) ( ) Point ((1,4) ) lies inside the circle, so ( array llll & 1+16-6-40+p & < 0 & p < 29 (iv) array ) From inequalities Eqs. (i), (ii), (iii) and (iv), we get (25 < p < 29 ) Hence, option (b) is correct.

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