## Question

Equation of the circle which passes through the origin, has its centre on the line *x* + *y* = 4 and cuts the circle

*x*^{2} + *y*^{2} – 4*x* + 2*y* + 4 = 0 orthogonally, is

### Solution

None of these.

Since the centre of the required circle lies on *x* + *y* = 4, let (*g*, 4 – *g*) be this centre. Since the circle passes through the origin, let its equation be

*x*^{2} + *y*^{2} – 2*gx* – 2(4 – *g*)*y* = 0

As this circle cuts the given circle orthogonally, we have

So that equation of the required circle is *x*^{2} + *y*^{2} – 4*x* – 4*y* = 0.

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