# If a circle passes through the point   and cuts the circle orthogonally, then the equation of the locus of its centre is Option 1) Option 2) Option 3) Option 4)

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)

This is incorrect option

Option 3)

This is correct option

Option 4)

This is incorrect option

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