The coordinates of the pole of the line lx + | vedclass

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Question

(B) Let the pole be $(x_1, y_1)$.The equation of the polar of the point $(x_1, y_1)$ with respect to the circle $x^2 + y^2 = 1$ is given by $x x_1 + y

Vedclass · Accepted Answer

$\left( -\frac{l}{n}, -\frac{m}{n} \right)$

Vedclass · Answer

(B) Let the pole be $(x_1, y_1)$.The equation of the polar of the point $(x_1, y_1)$ with respect to the circle $x^2 + y^2 = 1$ is given by $x x_1 + y y_1 = 1$,which can be rewritten as $x x_1 + y y_1 - 1 = 0$.We are given the line $lx + my + n = 0$,which can be rewritten as $lx + my = -n$,or $x(\frac{l}{-n}) + y(\frac{m}{-n}) = 1$.Comparing the two equations $x x_1 + y y_1 = 1$ and $x(\frac{l}{-n}) + y(\frac{m}{-n}) = 1$,we get:$x_1 = -\frac{l}{n}$ and $y_1 = -\frac{m}{n}$.Thus,the coordinates of the pole are $\left( -\frac{l}{n}, -\frac{m}{n} \right)$.

The coordinates of the pole of the line $lx + my + n = 0$ with respect to the circle $x^2 + y^2 = 1$ are:

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