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Question

# The equation of circle passing through the origin and cutting off equal intercepts of 4 units on the lines xy=0 can be

A
x(x4)+y(y4)=0
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B
x(x+4)+y(y4)=0
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C
x(x+4)+y(y+4)=0
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D
x(x4)+y(y+4)=0
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Solution

## The correct options are A x(x−4)+y(y−4)=0 B x(x+4)+y(y−4)=0 C x(x+4)+y(y+4)=0 D x(x−4)+y(y+4)=0 Given : xy=0 ⇒x=0 or y=0 Points on the line y=0 which is 4 units from the origin : A≡(4,0) and C≡(−4,0) Points on the line x=0 which is 4 units from the origin : B≡(0,4) and D≡(0,−4) Since both these lines are perpendicular, so, using diametric form for equation of circle with : AB as diameter is (x−4)(x−0)+(y−0)(y−4)=0, BC as diameter is (x−0)(x+4)+(y−4)(y−0)=0, CD as diameter is (x+4)(x−0)+(y−0)(y+4)=0, AD as diameter is (x−4)(x−0)+(y−0)(y+4)=0

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