A line lx + my + n = 0 meets the circle x^2 + | vedclass

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(B) Let the coordinates of point $R$ be $(h, k)$.The equation of the chord of contact of tangents drawn from $R(h, k)$ to the circle $x^2 + y^2 = a^2$

Vedclass · Accepted Answer

$\left( \frac{-a^2l}{n}, \frac{-a^2m}{n} \right)$

Vedclass · Answer

(B) Let the coordinates of point $R$ be $(h, k)$.The equation of the chord of contact of tangents drawn from $R(h, k)$ to the circle $x^2 + y^2 = a^2$ is given by $hx + ky = a^2$,or $hx + ky - a^2 = 0$.It is given that this chord of contact is the line $lx + my + n = 0$.Since both equations represent the same line,their coefficients must be proportional:$\frac{h}{l} = \frac{k}{m} = \frac{-a^2}{n}$.From this,we get:$h = \frac{-a^2l}{n}$ and $k = \frac{-a^2m}{n}$.Therefore,the coordinates of $R$ are $\left( \frac{-a^2l}{n}, \frac{-a^2m}{n} \right)$.

$A$ line $lx + my + n = 0$ meets the circle $x^2 + y^2 = a^2$ at the points $P$ and $Q$. The tangents drawn at the points $P$ and $Q$ meet at $R$. Then,the coordinates of $R$ are:

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