If the line lx + my + n = 0 is a tangent to t | vedclass

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(C) The condition for a line $lx + my + n = 0$ to be tangent to a circle $(x - h)^2 + (y - k)^2 = a^2$ is that the perpendicular distance from the cen

Vedclass · Accepted Answer

$(hl + km + n)^2 = a^2(l^2 + m^2)$

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(C) The condition for a line $lx + my + n = 0$ to be tangent to a circle $(x - h)^2 + (y - k)^2 = a^2$ is that the perpendicular distance from the center $(h, k)$ to the line must be equal to the radius $a$.The perpendicular distance $d$ is given by:$d = \frac{|lh + mk + n|}{\sqrt{l^2 + m^2}}$Setting $d = a$:$a = \frac{|lh + mk + n|}{\sqrt{l^2 + m^2}}$Squaring both sides:$a^2 = \frac{(lh + mk + n)^2}{l^2 + m^2}$Therefore:$(lh + mk + n)^2 = a^2(l^2 + m^2)$

If the line $lx + my + n = 0$ is a tangent to the circle $(x - h)^2 + (y - k)^2 = a^2$,then

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