If a circle passes through the point and cuts the circle orthogonally, then the equation of the locus of its centre is
As we learnt in
Orthogonality of two circle -
Two circles and are said to be orthogonal ,if tangents at their point of intersection include right angle.
- wherein
Let the variable circle is
x2 + y2 + 2gx + 2fy + C = 0
It passes through ( a, b)
a2+b2+2ga+2fb+c=0 -- (i)
It cuts x2 + y2 =p2 orthogonally.
so, c = p2
For locus of (-g, -f), Replace it by (x, y) in (i)
-2ax - 2by + (a2 + b2 + p2) = 0
so, 2ax + 2by - (a2 + b2 + p2) = 0
Option 1)
This is incorrect option
Option 2)
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Option 3)
This is correct option
Option 4)
This is incorrect option
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