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1)

Circle (s) touching x-axis at a distance 3 from the origin and having an intercept of length  27 on the y-axis is (are)


A) x2+y26x+8y+9=0

B) x2+y26x+7y+9=0

C) x2+y26x8y+9=0

D) x2+y26x7y+9=0

Answer:

Option A,C

Explanation:

Concept involved

1352021335_m1.JPG

 Here, thr length of intercept on y-axis 

             2f2c

 and if circle touches x-axis

      g2=c

 for     x2+y2+2gx+2fy+c=0

 here, x2+y2+2gx+2fy+c=0

1352021811_m2.JPG

 Passes through (3,0)

         9+6g+c=0  ........(i)

    g2=c    ..........(ii)

 and  2f2c=27

          f2c=7     .........(iii)

 From Eqs .(i) and (ii), we get

 g2+6g+9=0

    (g+3)2  =0

 g=-3

 and c=9     f2=16

 f=±4

      x2+y26x±8y+9=0