If the line lx + my = 1 is a tangent to the c | vedclass

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(B) The condition for the line $lx + my - 1 = 0$ to be a tangent to the circle ${x^2} + {y^2} = {a^2}$ is that the perpendicular distance from the cen

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$A$ circle

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(B) The condition for the line $lx + my - 1 = 0$ to be a tangent to the circle ${x^2} + {y^2} = {a^2}$ is that the perpendicular distance from the center $(0, 0)$ to the line must be equal to the radius $a$.Applying the formula for the distance from a point to a line: $\frac{|l(0) + m(0) - 1|}{\sqrt{l^2 + m^2}} = a$.This simplifies to $\frac{1}{\sqrt{l^2 + m^2}} = a$.Squaring both sides,we get $l^2 + m^2 = \frac{1}{a^2}$.Replacing $(l, m)$ with $(x, y)$,the locus is $x^2 + y^2 = \frac{1}{a^2}$,which represents a circle.

If the line $lx + my = 1$ is a tangent to the circle ${x^2} + {y^2} = {a^2}$,then the locus of the point $(l, m)$ is

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