CircleHard
Question
The locus of the centers of the circles which cut the circles x2 + y2 + 4x - 6y + 9 = 0 and x2 + y2 - 5x + 4y - 2 = 0 orthogonally is -
Options
A.9x + 10y - 7 = 0
B.x - y + 2 = 0
C.9x - 10y + 11 = 0
D.9x + 10y + 7 = 0
Solution
Let the centre of circle be (-g, -f)
Using condition of orthogonality :
2(g1g2 + f1f2) = C1 + C2
2
= - 2 + C .......(ii)
Subtract (ii) from (i)
2
= 11 ⇒ 9g - 10f = 11
replacing (-g) by h & (-f) by k.
- 9h + 10k = 11
⇒ 9x - 10y + 11 = 0
Using condition of orthogonality :
2(g1g2 + f1f2) = C1 + C2
2
= - 2 + C .......(ii)Subtract (ii) from (i)
2
= 11 ⇒ 9g - 10f = 11replacing (-g) by h & (-f) by k.
- 9h + 10k = 11
⇒ 9x - 10y + 11 = 0
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