The locus of the centre of the circle which cuts off intercepts of length $2 a$ and $2 b$ from x-axis and y-axis, respectively, is?

x + y = a + b

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x^{2} + y^{2} = a^{2} + b^{2}

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x^{2} - y^{2} = a^{2} - b^{2}

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x^{2} + y^{2} = a^{2} - b^{2}

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Solution

The correct option is B $x^{2} + y^{2} = a^{2} + b^{2}$
For the locus of the centre,

$\sqrt{{(α - 0)}^{2} + {(β - 0)}^{2}}$ $= \sqrt{a^{2} + b^{2}}$

$α^{2} + β^{2} = a^{2} + b^{2}$

so locus is,

$x^{2} + y^{2} = a^{2} + b^{2}$

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The locus of the centre of the circle which cuts off intercepts of length 2a and 2b from x-axis and y-axis, respectively, is?

The correct option is B x2+y2=a2+b2For the locus of the centre,√(α−0)2+(β−0)2=√a2+b2α2+β2=a2+b2so locus is,x2+y2=a2+b2

The locus of the centre of the circle which cuts off intercepts of length $2 a$ and $2 b$ from x-axis and y-axis, respectively, is?

The correct option is B $x^{2} + y^{2} = a^{2} + b^{2}$
For the locus of the centre,

$\sqrt{{(α - 0)}^{2} + {(β - 0)}^{2}}$ $= \sqrt{a^{2} + b^{2}}$

$α^{2} + β^{2} = a^{2} + b^{2}$

so locus is,

$x^{2} + y^{2} = a^{2} + b^{2}$