The locus of the centre of the circles which intersects the circles $x^{2} + y^{2} = 1$ and $x^{2} + y^{2} - 2 x + y = 0$ orthogonally is

a line whose equation is

2 x - y - 1 = 0

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a line whose equation is

2 x + y = 1

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a circle

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a pair oflines

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Solution

The correct option is A a line whose equation is $2 x - y - 1 = 0$
as property.
The locus of centre of circle cutting two given circle
orthogonally is the radial axis of two circles.
reqd equation is :-
$S_{1} - S_{2} = 0$
$∴$ radial axis of $x^{2} + y^{2} - 1 = 0$ and $x^{2} + y^{2} - 2 x + y = 0$ is
$\Rightarrow 2 x - y - 1 = 0$

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The locus of the centre of the circles which intersects the circles x2+y2=1 and x2+y2−2x+y=0 orthogonally is

The correct option is A a line whose equation is 2x−y−1=0as property.The locus of centre of circle cutting two given circleorthogonally is the radial axis of two circles.reqd equation is :- S1−S2=0∴ radial axis of x2+y2−1=0 and x2+y2−2x+y=0 is⇒2x−y−1=0

The locus of the centre of the circles which intersects the circles $x^{2} + y^{2} = 1$ and $x^{2} + y^{2} - 2 x + y = 0$ orthogonally is