ExamBro
ExamBro
JEE Advanced · Mathematics · 12. Circle

A circle S passes through the point (0, 1) and is orthogonal to the circles x-12+y2=16 and x 2 + y 2 = 1 . Then

  1. A Radius of S is 8
  2. B Radius of S is 7
  3. C Centre of S is (-7, 1)
  4. D Centre of S is (-8, 1)
Verified Solution

Answer & Solution

Correct Answer

(C) Centre of S is (-7, 1)

Step-by-step Solution

Detailed explanation

Given circles
x2+y2-2x-15=0
x2+y2-1=0
Radical axis x+7=0 ......(i)
Centre of circle lies on (i)
Let the centre be -7, k
Let equation be x2+y2+14x-2ky+c=0
Orthogonallity gives
- 14=c-15 c=1 .......(ii)
0, 11-2k+1=0 k=1
Hence radius = 72+k2-c= 49+1-1=7
Alternate Solution
Given circles x2+y2-2x-15=0
x2+y2-1=0
Let equation of circle x2+y2+2gx+2fy+c=0
Circle passes through (0, 1)
1+2f+c=0
Applying condition of orthogonality
-2g=c-15, 0=c-1
c=1, g=7, f= -1
r= 49+1-1=7; centre -7, 1
Same subject
Explore more questions on app
From JEE Advanced
Explore more questions on app