If a circle of radius R passes through the or | vedclass

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Question

Slope of $AB = \frac{{ - h}}{k}$

Equation of $AB$ is $hx + ky = {h^2} + {k^2}$

$A\left( {\frac{{{h^2} + {k^2}}}{h},0} \right),B\left(

Vedclass · Accepted Answer

${({x^2} + {y^2})^3} = 4{R^2}{x^2}{y^2}$

Vedclass · Answer

Slope of $AB = \frac{{ - h}}{k}$

Equation of $AB$ is $hx + ky = {h^2} + {k^2}$

$A\left( {\frac{{{h^2} + {k^2}}}{h},0} \right),B\left( {0,\frac{{{h^2} + {k^2}}}{k}} \right)$

$As,AB = 2R$

$ \Rightarrow {\left( {{h^2} + {k^2}} \right)^3} = 4{R^2}{h^2}{k^2}$

$ \Rightarrow {\left( {{x^2} + {y^2}} \right)^3} = 4{R^2}{x^2}{y^2}$

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B,$ then the locus of the foot of perpendicular from $O$ on $AB$ is

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